For reasons of transparency and collaborative opportunities, the analysis code is shared and annotated briefly. We highly recommend reading the manuscript before checking or using the analysis code. However, the most important, non-self-explanatory terms are defined below.
Study participants are divided into test-takers (of either the TMS or HAM-Nat) and incumbents, which refers to test-takers who reported enrollment and provided at least one measure of study success. Two outcome variables were used. First, PCGPA which refers to the grade point average over the assessments during the first two preclinical years of undergraduate training. Second, M1 which is the result of the first part of the medical licensing examination.
Due to data privacy restrictions of the student admission research consortium stav, data cannot be shared with external researchers. Requests to access this dataset should be directed to kontakt(at)projekt-stav.de
#Number of participants
study_participants <- data %>% filter(!is.na(Gender) & !is.na(Age) & !is.na(GPA) & (!is.na(PCGPA) | !is.na(M1)) & (!is.na(TMS_total) | !is.na(HAMNat_total)))
nrow(study_participants)## [1] 2113#Year of application
table(study_participants$year_of_application)##
## 2017 2018 2019 2020 2021 2022
## 6 44 66 556 851 590round(prop.table(table(study_participants$year_of_application)), 4)##
## 2017 2018 2019 2020 2021 2022
## 0.0028 0.0208 0.0312 0.2631 0.4027 0.2792#Gender is coded with 1 = female, 2 = male, and 3 = gender-diverse.
psych::describe(data_TMS_Incumbents[, c('Gender', 'Age', 'GPA','TMS_total', 'PCGPA', 'M1')], fast = TRUE)## vars n mean sd min max range se
## Gender 1 1880 1.31 0.47 1.0 3 2.0 0.01
## Age 2 1880 20.48 2.52 16.0 43 27.0 0.06
## GPA 3 1880 1.52 0.45 0.9 4 3.1 0.01
## TMS_total 4 1880 107.43 7.97 82.0 129 47.0 0.18
## PCGPA 5 1867 2.17 0.64 1.0 4 3.0 0.01
## M1 6 377 2.39 0.81 1.0 5 4.0 0.04table(data_TMS_Incumbents$Gender)##
## 1 2 3
## 1310 563 7round(prop.table(table(data_TMS_Incumbents$Gender)), 4)##
## 1 2 3
## 0.6968 0.2995 0.0037psych::describe(data_TMS_Testtakers[, c('Gender', 'Age', 'GPA','TMS_total')], fast = TRUE)## vars n mean sd min max range se
## Gender 1 8796 1.27 0.45 1.0 3 2.0 0.00
## Age 2 8796 20.77 2.37 16.0 52 36.0 0.03
## GPA 3 8796 1.70 0.47 0.9 4 3.1 0.00
## TMS_total 4 8796 102.47 9.43 0.0 129 129.0 0.10table(data_TMS_Testtakers$Gender)##
## 1 2 3
## 6447 2327 22round(prop.table(table(data_TMS_Testtakers$Gender)), 4)##
## 1 2 3
## 0.7329 0.2646 0.0025#Excluding gender-diverse participants due to a insufficient sample size.
data_TMS_Incumbents <-(subset(data_TMS_Incumbents, Gender != 3))
data_TMS_Testtakers <-(subset(data_TMS_Testtakers, Gender != 3))
#Correlation matrices
rcorr(as.matrix(data_TMS_Incumbents[ , c('Gender', 'Age', 'GPA','TMS_total', 'PCGPA', 'M1')]))## Gender Age GPA TMS_total PCGPA M1
## Gender 1.00 0.06 0.10 0.06 -0.09 -0.12
## Age 0.06 1.00 0.59 -0.16 0.12 0.18
## GPA 0.10 0.59 1.00 -0.10 0.14 0.21
## TMS_total 0.06 -0.16 -0.10 1.00 -0.18 -0.18
## PCGPA -0.09 0.12 0.14 -0.18 1.00 0.64
## M1 -0.12 0.18 0.21 -0.18 0.64 1.00
##
## n
## Gender Age GPA TMS_total PCGPA M1
## Gender 1873 1873 1873 1873 1860 375
## Age 1873 1873 1873 1873 1860 375
## GPA 1873 1873 1873 1873 1860 375
## TMS_total 1873 1873 1873 1873 1860 375
## PCGPA 1860 1860 1860 1860 1860 362
## M1 375 375 375 375 362 375
##
## P
## Gender Age GPA TMS_total PCGPA M1
## Gender 0.0071 0.0000 0.0157 0.0001 0.0183
## Age 0.0071 0.0000 0.0000 0.0000 0.0006
## GPA 0.0000 0.0000 0.0000 0.0000 0.0000
## TMS_total 0.0157 0.0000 0.0000 0.0000 0.0004
## PCGPA 0.0001 0.0000 0.0000 0.0000 0.0000
## M1 0.0183 0.0006 0.0000 0.0004 0.0000rcorr(as.matrix(data_TMS_Testtakers[ , c('Gender', 'Age', 'GPA','TMS_total')]))## Gender Age GPA TMS_total
## Gender 1.00 0.05 0.03 0.09
## Age 0.05 1.00 0.46 -0.17
## GPA 0.03 0.46 1.00 -0.28
## TMS_total 0.09 -0.17 -0.28 1.00
##
## n= 8774
##
##
## P
## Gender Age GPA TMS_total
## Gender 0.0000 0.0018 0.0000
## Age 0.0000 0.0000 0.0000
## GPA 0.0018 0.0000 0.0000
## TMS_total 0.0000 0.0000 0.0000#Gender is coded with 1 = female, 2 = male, and 3 = gender-diverse.
psych::describe(data_HAMNat_Incumbents[, c('Gender', 'Age', 'GPA','HAMNat_total', 'PCGPA', 'M1')], fast = TRUE)## vars n mean sd min max range se
## Gender 1 706 1.36 0.48 1.00 2.0 1.00 0.02
## Age 2 706 21.21 2.57 17.00 37.0 20.00 0.10
## GPA 3 706 1.63 0.43 0.90 3.4 2.50 0.02
## HAMNat_total 4 706 0.77 0.92 -2.63 2.9 5.52 0.03
## PCGPA 5 699 2.14 0.64 1.00 4.0 3.00 0.02
## M1 6 233 2.28 0.84 1.00 4.0 3.00 0.06table(data_HAMNat_Incumbents$Gender)##
## 1 2
## 455 251round(prop.table(table(data_HAMNat_Incumbents$Gender)), 4)##
## 1 2
## 0.6445 0.3555psych::describe(data_HAMNat_Testtakers[, c('Gender', 'Age', 'GPA','HAMNat_total')], fast = TRUE)## vars n mean sd min max range se
## Gender 1 5020 1.31 0.47 1.00 3.0 2.00 0.01
## Age 2 5020 21.31 2.64 15.00 51.0 36.00 0.04
## GPA 3 5020 1.80 0.48 0.90 3.6 2.70 0.01
## HAMNat_total 4 5020 0.28 0.87 -2.99 2.9 5.89 0.01table(data_HAMNat_Testtakers$Gender)##
## 1 2 3
## 3486 1525 9round(prop.table(table(data_HAMNat_Testtakers$Gender)), 4)##
## 1 2 3
## 0.6944 0.3038 0.0018#Excluding gender-diverse participants due to a insufficient sample size.
data_HAMNat_Incumbents <-(subset(data_HAMNat_Incumbents, Gender != 3))
data_HAMNat_Testtakers <-(subset(data_HAMNat_Testtakers, Gender != 3))
#Correlation matrices
rcorr(as.matrix(data_HAMNat_Incumbents[ , c('Gender', 'Age', 'GPA','HAMNat_total', 'PCGPA', 'M1')]))## Gender Age GPA HAMNat_total PCGPA M1
## Gender 1.00 0.04 0.09 0.20 -0.03 -0.10
## Age 0.04 1.00 0.55 -0.06 0.07 0.24
## GPA 0.09 0.55 1.00 -0.08 0.15 0.28
## HAMNat_total 0.20 -0.06 -0.08 1.00 -0.35 -0.46
## PCGPA -0.03 0.07 0.15 -0.35 1.00 0.69
## M1 -0.10 0.24 0.28 -0.46 0.69 1.00
##
## n
## Gender Age GPA HAMNat_total PCGPA M1
## Gender 706 706 706 706 699 233
## Age 706 706 706 706 699 233
## GPA 706 706 706 706 699 233
## HAMNat_total 706 706 706 706 699 233
## PCGPA 699 699 699 699 699 226
## M1 233 233 233 233 226 233
##
## P
## Gender Age GPA HAMNat_total PCGPA M1
## Gender 0.3127 0.0140 0.0000 0.4283 0.1386
## Age 0.3127 0.0000 0.0917 0.0627 0.0003
## GPA 0.0140 0.0000 0.0317 0.0001 0.0000
## HAMNat_total 0.0000 0.0917 0.0317 0.0000 0.0000
## PCGPA 0.4283 0.0627 0.0001 0.0000 0.0000
## M1 0.1386 0.0003 0.0000 0.0000 0.0000rcorr(as.matrix(data_HAMNat_Testtakers[ , c('Gender', 'Age', 'GPA','HAMNat_total')]))## Gender Age GPA HAMNat_total
## Gender 1.00 0.02 0.03 0.20
## Age 0.02 1.00 0.41 -0.05
## GPA 0.03 0.41 1.00 -0.28
## HAMNat_total 0.20 -0.05 -0.28 1.00
##
## n= 5011
##
##
## P
## Gender Age GPA HAMNat_total
## Gender 0.1478 0.0622 0.0000
## Age 0.1478 0.0000 0.0004
## GPA 0.0622 0.0000 0.0000
## HAMNat_total 0.0000 0.0004 0.0000#Enrollment is coded with 1 = true (i.e., incumbents) and 2 = false (i.e., test-takers).
#Age
leveneTest(data_TMS_Testtakers$Age, data_TMS_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 2.0183 0.1554
## 8257t.test(Age ~ Enrollment, var.equal = TRUE, alternative = "less", data = data_TMS_Testtakers)##
## Two Sample t-test
##
## data: Age by Enrollment
## t = -6.9767, df = 8257, p-value = 1.628e-12
## alternative hypothesis: true difference in means between group 1 and group 2 is less than 0
## 95 percent confidence interval:
## -Inf -0.3318706
## sample estimates:
## mean in group 1 mean in group 2
## 20.47037 20.90464data_TMS_Testtakers %>% cohens_d(Age ~ Enrollment, var.equal = TRUE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 Age 1 2 -0.183 1873 6386 negligible#High-school GPA
leveneTest(data_TMS_Testtakers$GPA, data_TMS_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.9626 0.1613
## 8257t.test(GPA ~ Enrollment, var.equal = TRUE, alternative = "less", data = data_TMS_Testtakers)##
## Two Sample t-test
##
## data: GPA by Enrollment
## t = -20.841, df = 8257, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 1 and group 2 is less than 0
## 95 percent confidence interval:
## -Inf -0.2290912
## sample estimates:
## mean in group 1 mean in group 2
## 1.523011 1.771735data_TMS_Testtakers %>% cohens_d(GPA ~ Enrollment, var.equal = TRUE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 GPA 1 2 -0.548 1873 6386 moderate#TMS score
leveneTest(data_TMS_Testtakers$TMS_total, data_TMS_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 47.773 5.14e-12 ***
## 8257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1t.test(TMS_total ~ Enrollment, var.equal = FALSE, alternative = "greater", data = data_TMS_Testtakers)##
## Welch Two Sample t-test
##
## data: TMS_total by Enrollment
## t = 31.028, df = 3480.4, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 1 and group 2 is greater than 0
## 95 percent confidence interval:
## 6.391978 Inf
## sample estimates:
## mean in group 1 mean in group 2
## 107.4170 100.6671data_TMS_Testtakers %>% cohens_d(TMS_total ~ Enrollment, var.equal = FALSE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 TMS_total 1 2 0.782 1873 6386 moderate#Gender
chisq.test(data_TMS_Testtakers$Gender, data_TMS_Testtakers$Enrollment)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: data_TMS_Testtakers$Gender and data_TMS_Testtakers$Enrollment
## X-squared = 14.71, df = 1, p-value = 0.0001254cramerV(data_TMS_Testtakers$Gender, data_TMS_Testtakers$Enrollment)## Cramer V
## 0.04126#Enrollment is coded with 1 = true (i.e., incumbents) and 2 = false (i.e., test-takers).
#Age
leveneTest(data_HAMNat_Testtakers$Age, data_HAMNat_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.0734 0.3002
## 4862t.test(Age ~ Enrollment, var.equal = TRUE, alternative = "less", data = data_HAMNat_Testtakers)##
## Two Sample t-test
##
## data: Age by Enrollment
## t = -1.0637, df = 4862, p-value = 0.1438
## alternative hypothesis: true difference in means between group 1 and group 2 is less than 0
## 95 percent confidence interval:
## -Inf 0.0618495
## sample estimates:
## mean in group 1 mean in group 2
## 21.21105 21.32419data_HAMNat_Testtakers %>% cohens_d(Age ~ Enrollment, var.equal = TRUE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 Age 1 2 -0.0433 706 4158 negligible#High-school GPA
leveneTest(data_HAMNat_Testtakers$GPA, data_HAMNat_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 11.741 0.0006163 ***
## 4862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1t.test(GPA ~ Enrollment, var.equal = FALSE, alternative = "less", data = data_HAMNat_Testtakers)##
## Welch Two Sample t-test
##
## data: GPA by Enrollment
## t = -11.778, df = 1014.6, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 1 and group 2 is less than 0
## 95 percent confidence interval:
## -Inf -0.181961
## sample estimates:
## mean in group 1 mean in group 2
## 1.628754 1.840284data_HAMNat_Testtakers %>% cohens_d(GPA ~ Enrollment, var.equal = FALSE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 GPA 1 2 -0.464 706 4158 small#HAM-Nat score
leveneTest(data_HAMNat_Testtakers$HAMNat_total, data_HAMNat_Testtakers$Enrollment)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 24.89 6.282e-07 ***
## 4862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1t.test(HAMNat_total ~ Enrollment, var.equal = FALSE, alternative = "greater", data = data_HAMNat_Testtakers)##
## Welch Two Sample t-test
##
## data: HAMNat_total by Enrollment
## t = 16.135, df = 912.23, p-value < 2.2e-16
## alternative hypothesis: true difference in means between group 1 and group 2 is greater than 0
## 95 percent confidence interval:
## 0.5329499 Inf
## sample estimates:
## mean in group 1 mean in group 2
## 0.7747497 0.1812355data_HAMNat_Testtakers %>% cohens_d(HAMNat_total ~ Enrollment, var.equal = FALSE)## # A tibble: 1 × 7
## .y. group1 group2 effsize n1 n2 magnitude
## * <chr> <chr> <chr> <dbl> <int> <int> <ord>
## 1 HAMNat_total 1 2 0.679 706 4158 moderate#Gender
chisq.test(data_HAMNat_Testtakers$Gender, data_HAMNat_Testtakers$Enrollment)##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: data_HAMNat_Testtakers$Gender and data_HAMNat_Testtakers$Enrollment
## X-squared = 9.2987, df = 1, p-value = 0.002293cramerV(data_HAMNat_Testtakers$Gender, data_HAMNat_Testtakers$Enrollment)## Cramer V
## 0.0437#Criterion: PCGPA
#Models
lm_TMS_1 <- lm(PCGPA ~ Gender + Age, data = data_TMS_Incumbents)
lm_TMS_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_TMS_Incumbents)
lm_TMS_2b <- lm(PCGPA ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
lm_TMS_3 <- lm(PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
#Results
summary(lm_TMS_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.72981 -0.43379 -0.09653 0.40937 1.86621
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.705443 0.125536 13.585 < 2e-16 ***
## Gender -0.136305 0.032150 -4.240 2.35e-05 ***
## Age 0.031369 0.005866 5.347 1.00e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6351 on 1857 degrees of freedom
## (13 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.02309, Adjusted R-squared: 0.02204
## F-statistic: 21.95 on 2 and 1857 DF, p-value: 3.797e-10summary(lm_TMS_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.72401 -0.45387 -0.09312 0.41270 1.84397
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.832711 0.128116 14.305 < 2e-16 ***
## Gender -0.147989 0.032095 -4.611 4.28e-06 ***
## Age 0.012371 0.007224 1.712 0.087 .
## GPA 0.181734 0.040725 4.462 8.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6319 on 1856 degrees of freedom
## (13 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.03346, Adjusted R-squared: 0.0319
## F-statistic: 21.42 on 3 and 1856 DF, p-value: 1.226e-13summary(lm_TMS_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52258 -0.42823 -0.09179 0.40834 1.92407
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.160364 0.249324 12.676 < 2e-16 ***
## Gender -0.121259 0.031853 -3.807 0.000145 ***
## Age 0.024821 0.005879 4.222 2.54e-05 ***
## TMS_total -0.012478 0.001855 -6.728 2.29e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6277 on 1856 degrees of freedom
## (13 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.04635, Adjusted R-squared: 0.04481
## F-statistic: 30.07 on 3 and 1856 DF, p-value: < 2.2e-16summary(lm_TMS_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.51844 -0.44050 -0.08705 0.40149 1.89607
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.274543 0.249408 13.129 < 2e-16 ***
## Gender -0.132858 0.031801 -4.178 3.08e-05 ***
## Age 0.006195 0.007199 0.861 0.39
## GPA 0.178644 0.040253 4.438 9.61e-06 ***
## TMS_total -0.012384 0.001846 -6.710 2.57e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6246 on 1855 degrees of freedom
## (13 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.05637, Adjusted R-squared: 0.05433
## F-statistic: 27.7 on 4 and 1855 DF, p-value: < 2.2e-16lm.beta(lm_TMS_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age
## NA -0.09743258 0.12288789lm.beta(lm_TMS_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA
## NA -0.10578452 0.04846357 0.12671626lm.beta(lm_TMS_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age TMS_total
## NA -0.08667757 0.09723666 -0.15490131lm.beta(lm_TMS_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA TMS_total
## NA -0.09496828 0.02427030 0.12456185 -0.15373815anova(lm_TMS_1, lm_TMS_2a, lm_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1857 749.08
## 2 1856 741.13 1 7.9518 20.386 6.728e-06 ***
## 3 1855 723.57 1 17.5629 45.026 2.575e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_1, lm_TMS_2b, lm_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + TMS_total
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1857 749.08
## 2 1856 731.25 1 17.8320 45.716 1.826e-11 ***
## 3 1855 723.57 1 7.6827 19.696 9.613e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_TMS_M1_1 <- lm(M1 ~ Gender + Age, data = data_TMS_Incumbents)
lm_TMS_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_TMS_Incumbents)
lm_TMS_M1_2b <- lm(M1 ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
lm_TMS_M1_3 <- lm(M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
#Results
summary(lm_TMS_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55701 -0.55701 0.00301 0.56302 2.62304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.46618 0.35863 4.088 5.33e-05 ***
## Gender -0.22953 0.09003 -2.550 0.0112 *
## Age 0.06002 0.01680 3.573 0.0004 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7931 on 372 degrees of freedom
## (1498 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.04751, Adjusted R-squared: 0.04239
## F-statistic: 9.278 on 2 and 372 DF, p-value: 0.000117summary(lm_TMS_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.62231 -0.59105 -0.01738 0.57135 2.65241
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.70498 0.36588 4.660 4.42e-06 ***
## Gender -0.25673 0.08978 -2.859 0.00448 **
## Age 0.02206 0.02160 1.021 0.30773
## GPA 0.36933 0.13391 2.758 0.00610 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7861 on 371 degrees of freedom
## (1498 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.06665, Adjusted R-squared: 0.0591
## F-statistic: 8.831 on 3 and 371 DF, p-value: 1.144e-05summary(lm_TMS_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.59396 -0.59744 0.00334 0.59383 2.64363
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.421643 0.671392 5.096 5.53e-07 ***
## Gender -0.244043 0.088857 -2.746 0.006318 **
## Age 0.054412 0.016642 3.270 0.001178 **
## TMS_total -0.017176 0.005013 -3.426 0.000681 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7819 on 371 degrees of freedom
## (1498 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.07672, Adjusted R-squared: 0.06926
## F-statistic: 10.28 on 3 and 371 DF, p-value: 1.632e-06summary(lm_TMS_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.57633 -0.60591 0.01654 0.60641 2.66975
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.546989 0.668132 5.309 1.91e-07 ***
## Gender -0.268457 0.088699 -3.027 0.00265 **
## Age 0.019637 0.021336 0.920 0.35799
## GPA 0.341066 0.132466 2.575 0.01042 *
## TMS_total -0.016340 0.004986 -3.277 0.00115 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.776 on 370 degrees of freedom
## (1498 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.09297, Adjusted R-squared: 0.08317
## F-statistic: 9.481 on 4 and 370 DF, p-value: 2.629e-07lm.beta(lm_TMS_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age
## NA -0.1291155 0.1809318lm.beta(lm_TMS_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA
## NA -0.14441749 0.06651478 0.18057005lm.beta(lm_TMS_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + TMS_total, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age TMS_total
## NA -0.1372794 0.1640365 -0.1719738lm.beta(lm_TMS_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA TMS_total
## NA -0.15101284 0.05919872 0.16675012 -0.16360336anova(lm_TMS_M1_1, lm_TMS_M1_2a, lm_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 372 233.99
## 2 371 229.28 1 4.7014 7.8069 0.005476 **
## 3 370 222.82 1 6.4670 10.7387 0.001148 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_M1_1, lm_TMS_M1_2b, lm_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + TMS_total
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 372 233.99
## 2 371 226.81 1 7.1761 11.9162 0.0006208 ***
## 3 370 222.82 1 3.9923 6.6294 0.0104190 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Models
lm_HAMNat_1 <- lm(PCGPA ~ Gender + Age, data = data_HAMNat_Incumbents)
lm_HAMNat_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
lm_HAMNat_2b <- lm(PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
lm_HAMNat_3 <- lm(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
#Results
summary(lm_HAMNat_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2776 -0.4356 -0.1098 0.3999 1.8289
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.824051 0.208684 8.741 <2e-16 ***
## Gender -0.043536 0.050168 -0.868 0.3858
## Age 0.017754 0.009361 1.897 0.0583 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6347 on 696 degrees of freedom
## (7 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.006037, Adjusted R-squared: 0.003181
## F-statistic: 2.114 on 2 and 696 DF, p-value: 0.1216summary(lm_HAMNat_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2707 -0.4631 -0.0981 0.4061 1.8935
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.917613 0.208728 9.187 < 2e-16 ***
## Gender -0.058175 0.049941 -1.165 0.244467
## Age -0.003489 0.011089 -0.315 0.753130
## GPA 0.231320 0.066011 3.504 0.000487 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6296 on 695 degrees of freedom
## (7 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.02329, Adjusted R-squared: 0.01908
## F-statistic: 5.525 on 3 and 695 DF, p-value: 0.0009418summary(lm_HAMNat_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.34885 -0.42914 -0.05229 0.41633 1.68216
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.019693 0.197122 10.246 <2e-16 ***
## Gender 0.050308 0.048127 1.045 0.296
## Age 0.011477 0.008819 1.301 0.194
## HAMNat_total -0.243363 0.025186 -9.662 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5963 on 695 degrees of freedom
## (7 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1237, Adjusted R-squared: 0.12
## F-statistic: 32.72 on 3 and 695 DF, p-value: < 2.2e-16summary(lm_HAMNat_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.34156 -0.42910 -0.05917 0.41644 1.67121
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.090335 0.197434 10.587 < 2e-16 ***
## Gender 0.036315 0.048085 0.755 0.45037
## Age -0.005463 0.010446 -0.523 0.60116
## GPA 0.186079 0.062356 2.984 0.00294 **
## HAMNat_total -0.237614 0.025118 -9.460 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.593 on 694 degrees of freedom
## (7 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1349, Adjusted R-squared: 0.1299
## F-statistic: 27.04 on 4 and 694 DF, p-value: < 2.2e-16lm.beta(lm_HAMNat_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age
## NA -0.03282007 0.07172846lm.beta(lm_HAMNat_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA
## NA -0.04385613 -0.01409691 0.15754123lm.beta(lm_HAMNat_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age HAMNat_total
## NA 0.03792524 0.04636843 -0.35102601lm.beta(lm_HAMNat_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA HAMNat_total
## NA 0.02737638 -0.02207231 0.12672964 -0.34273374anova(lm_HAMNat_1, lm_HAMNat_2a, lm_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 696 280.36
## 2 695 275.50 1 4.8677 13.843 0.0002148 ***
## 3 694 244.03 1 31.4663 89.487 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_1, lm_HAMNat_2b, lm_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + HAMNat_total
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 696 280.36
## 2 695 247.16 1 33.203 94.4255 < 2.2e-16 ***
## 3 694 244.03 1 3.131 8.9052 0.002943 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_HAMNat_M1_1 <- lm(M1 ~ Gender + Age, data = data_HAMNat_Incumbents)
lm_HAMNat_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
lm_HAMNat_M1_2b <- lm(M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
lm_HAMNat_M1_3 <- lm(M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
#Results
summary(lm_HAMNat_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7526 -0.6477 -0.1477 0.5912 2.0116
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.88922 0.44851 1.983 0.048599 *
## Gender -0.20681 0.11043 -1.873 0.062374 .
## Age 0.07962 0.02050 3.885 0.000134 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8174 on 230 degrees of freedom
## (473 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.07046, Adjusted R-squared: 0.06238
## F-statistic: 8.718 on 2 and 230 DF, p-value: 0.0002242summary(lm_HAMNat_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.71681 -0.63011 -0.08558 0.61826 2.09255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.08021 0.44543 2.425 0.01608 *
## Gender -0.22828 0.10879 -2.098 0.03696 *
## Age 0.03747 0.02455 1.526 0.12832
## GPA 0.44532 0.14819 3.005 0.00295 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8035 on 229 degrees of freedom
## (473 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1057, Adjusted R-squared: 0.09401
## F-statistic: 9.025 on 3 and 229 DF, p-value: 1.132e-05summary(lm_HAMNat_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.60131 -0.54350 -0.04737 0.53397 2.16261
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.40624 0.40896 3.439 0.000695 ***
## Gender -0.04032 0.10171 -0.396 0.692175
## Age 0.06314 0.01855 3.403 0.000786 ***
## HAMNat_total -0.42216 0.05652 -7.470 1.68e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7346 on 229 degrees of freedom
## (473 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2428
## F-statistic: 25.79 on 3 and 229 DF, p-value: 2.06e-14summary(lm_HAMNat_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.57799 -0.55069 -0.02762 0.50075 2.04989
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.54485 0.40681 3.798 0.000187 ***
## Gender -0.06283 0.10071 -0.624 0.533325
## Age 0.02953 0.02217 1.332 0.184194
## GPA 0.36037 0.13418 2.686 0.007772 **
## HAMNat_total -0.40914 0.05598 -7.309 4.5e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7248 on 228 degrees of freedom
## (473 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2755, Adjusted R-squared: 0.2628
## F-statistic: 21.67 on 4 and 228 DF, p-value: 3.595e-15lm.beta(lm_HAMNat_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age
## NA -0.1195348 0.2479617lm.beta(lm_HAMNat_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA
## NA -0.1319463 0.1166899 0.2300913lm.beta(lm_HAMNat_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age HAMNat_total
## NA -0.02330468 0.19661701 -0.43945205lm.beta(lm_HAMNat_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_Incumbents)
##
## Standardized Coefficients::
## (Intercept) Gender Age GPA HAMNat_total
## NA -0.03631674 0.09197143 0.18619714 -0.42589705anova(lm_HAMNat_M1_1, lm_HAMNat_M1_2a, lm_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 230 153.69
## 2 229 147.86 1 5.8304 11.097 0.001008 **
## 3 228 119.79 1 28.0680 53.423 4.499e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_M1_1, lm_HAMNat_M1_2b, lm_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + HAMNat_total
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 230 153.69
## 2 229 123.58 1 30.1090 57.3081 9.175e-13 ***
## 3 228 119.79 1 3.7894 7.2126 0.007772 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Correcting for range restriction
data_TMS_Incumbents$Gender <- as.numeric(data_TMS_Incumbents$Gender)
Cov_Mat_TMS_Incumbents <- cov((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, TMS_total, PCGPA)), use = "complete.obs")
Cor_Mat_TMS_Incumbents <- cor((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, TMS_total, PCGPA)), use = "complete.obs")
Cov_Mat_TMS_Testtakers <- cov((dplyr::select(data_TMS_Testtakers, Gender, Age, GPA, TMS_total)))
Cor_Mat_TMS_Testtakers <- cor((dplyr::select(data_TMS_Testtakers, Gender, Age, GPA, TMS_total)))
Cor_Mat_TMS_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_TMS_Incumbents, vnp = Cov_Mat_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_Incumbents_Corr) <- colnames(Cor_Mat_TMS_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'PCGPA')
#Models
lm_TMS_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_1), plot = F)
lm_TMS_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_2a), plot = F)
lm_TMS_2b_corr <- lmCor(PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_2b), plot = F)
lm_TMS_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_3), plot = F)
#Results
lm_TMS_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.11 0.02 -4.63 4.0e-06 -0.15 -0.06 1 0.01
## Age 0.11 0.02 4.94 8.4e-07 0.07 0.16 1 0.01
##
## Residual Standard Error = 0.99 with 1857 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.15 0.02 0.15 0.02 0.02 0.01 21.79 2 1857 4.43e-10lm_TMS_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.11 0.02 -4.76 2.1e-06 -0.15 -0.06 1.00 0.01
## Age 0.03 0.03 1.32 1.9e-01 -0.02 0.08 1.27 0.00
## GPA 0.17 0.03 6.79 1.5e-11 0.12 0.22 1.27 0.03
##
## Residual Standard Error = 0.98 with 1856 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.22 0.05 0.2 0.04 0.05 0.01 30.25 3 1856 4.31e-19lm_TMS_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.09 0.02 -3.83 1.3e-04 -0.13 -0.04 1.01 0.01
## Age 0.08 0.02 3.37 7.7e-04 0.03 0.12 1.04 0.01
## TMS_total -0.21 0.02 -9.00 5.4e-19 -0.25 -0.16 1.04 0.05
##
## Residual Standard Error = 0.97 with 1856 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.25 0.06 0.24 0.06 0.06 0.01 42.15 3 1856 2.39e-26lm_TMS_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.09 0.02 -4.02 6.0e-05 -0.13 -0.05 1.01 0.01
## Age 0.02 0.03 0.90 3.7e-01 -0.03 0.07 1.28 0.00
## GPA 0.13 0.03 4.98 7.0e-07 0.08 0.18 1.34 0.02
## TMS_total -0.18 0.02 -7.70 2.2e-14 -0.23 -0.13 1.10 0.04
##
## Residual Standard Error = 0.96 with 1855 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.28 0.08 0.26 0.07 0.07 0.01 38.21 4 1855 9.12e-31anova(lm_TMS_1_corr, lm_TMS_2a_corr, lm_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 1857 1816.373 NA NA NA NA
## 2 1856 1772.336 1 44.03699 47.56314 7.277322e-12
## 3 1855 1717.477 1 54.85830 59.25094 2.240550e-14anova(lm_TMS_1_corr, lm_TMS_2b_corr, lm_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 1857 1816.373 NA NA NA NA
## 2 1856 1740.420 1 75.95317 82.03492 3.295580e-19
## 3 1855 1717.477 1 22.94212 24.77915 7.024183e-07#Criterion: M1
#Correcting for range restriction
Cov_Mat_TMS_Incumbents_M1 <- cov((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, TMS_total, M1)), use = "complete.obs")
Cor_Mat_TMS_Incumbents_M1 <- cor((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, TMS_total, M1)), use = "complete.obs")
Cor_Mat_TMS_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_TMS_Incumbents_M1, vnp = Cov_Mat_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_Incumbents_Corr_M1) <- colnames(Cor_Mat_TMS_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'M1')
#Models
lm_TMS_M1_1_corr <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_M1_1), plot = F)
lm_TMS_M1_2a_corr <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_M1_2a), plot = F)
lm_TMS_M1_2b_corr <- lmCor(M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_M1_2b), plot = F)
lm_TMS_M1_3_corr <- lmCor(M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_M1_3), plot = F)
#Results
lm_TMS_M1_1_corr## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.16 0.05 -3.15 0.00180 -0.26 -0.06 1 0.02
## Age 0.18 0.05 3.52 0.00049 0.08 0.28 1 0.03
##
## Residual Standard Error = 0.98 with 372 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.23 0.05 0.23 0.05 0.05 0.02 10.59 2 372 3.35e-05lm_TMS_M1_2a_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.16 0.05 -3.27 1.2e-03 -0.26 -0.06 1.00 0.02
## Age 0.07 0.06 1.22 2.2e-01 -0.04 0.18 1.27 0.01
## GPA 0.24 0.06 4.30 2.2e-05 0.13 0.35 1.27 0.06
##
## Residual Standard Error = 0.95 with 371 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.31 0.1 0.3 0.09 0.09 0.03 13.56 3 371 2.05e-08lm_TMS_M1_2b_corr## Call: lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.14 0.05 -2.78 5.7e-03 -0.23 -0.04 1.01 0.02
## Age 0.14 0.05 2.75 6.3e-03 0.04 0.24 1.04 0.02
## TMS_total -0.23 0.05 -4.50 9.3e-06 -0.32 -0.13 1.04 0.06
##
## Residual Standard Error = 0.95 with 371 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.32 0.1 0.31 0.1 0.1 0.03 14.16 3 371 9.28e-09lm_TMS_M1_3_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.14 0.05 -2.93 0.00360 -0.24 -0.05 1.01 0.02
## Age 0.06 0.05 1.02 0.31000 -0.05 0.16 1.28 0.01
## GPA 0.19 0.06 3.43 0.00067 0.08 0.30 1.34 0.05
## TMS_total -0.19 0.05 -3.67 0.00028 -0.29 -0.09 1.10 0.05
##
## Residual Standard Error = 0.94 with 370 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.36 0.13 0.35 0.12 0.12 0.03 13.87 4 370 1.49e-10anova(lm_TMS_M1_1_corr, lm_TMS_M1_2a_corr, lm_TMS_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 372 353.8443 NA NA NA NA
## 2 371 337.0371 1 16.80716 19.12129 1.595519e-05
## 3 370 325.2212 1 11.81595 13.44286 2.819525e-04anova(lm_TMS_M1_1_corr, lm_TMS_M1_2b_corr, lm_TMS_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 372 353.8443 NA NA NA NA
## 2 371 335.5664 1 18.27785 20.79448 6.955298e-06
## 3 370 325.2212 1 10.34526 11.76967 6.699751e-04#Criterion: PCGPA
#Correcting for range restriction
Cov_Mat_HAMNat_Incumbents <- cov((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, HAMNat_total, PCGPA)), use = "complete.obs")
Cor_Mat_HAMNat_Incumbents <- cor((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, HAMNat_total, PCGPA)), use = "complete.obs")
Cov_Mat_HAMNat_Testtakers <- cov((dplyr::select(data_HAMNat_Testtakers, Gender, Age, GPA, HAMNat_total)))
Cor_Mat_HAMNat_Testtakers <- cor((dplyr::select(data_HAMNat_Testtakers, Gender, Age, GPA, HAMNat_total)))
Cor_Mat_HAMNat_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_HAMNat_Incumbents, vnp = Cov_Mat_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_Incumbents_Corr) <- colnames(Cor_Mat_HAMNat_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'PCGPA')
#Models
lm_HAMNat_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_1), plot = F)
lm_HAMNat_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_2a), plot = F)
lm_HAMNat_2b_corr <- lmCor(PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_2b), plot = F)
lm_HAMNat_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_3), plot = F)
#Results
lm_HAMNat_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.04 0.04 -0.96 0.34 -0.11 0.04 1 0
## Age 0.05 0.04 1.36 0.17 -0.02 0.13 1 0
##
## Residual Standard Error = 1 with 696 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.06 0 0.06 0 0 0 1.36 2 696 0.258lm_HAMNat_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.04 0.04 -1.10 2.7e-01 -0.11 0.03 1.0 0.00
## Age -0.05 0.04 -1.16 2.5e-01 -0.13 0.03 1.2 0.00
## GPA 0.24 0.04 5.98 3.6e-09 0.16 0.32 1.2 0.05
##
## Residual Standard Error = 0.98 with 695 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.23 0.05 0.16 0.03 0.05 0.02 12.86 3 695 3.49e-08lm_HAMNat_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.04 0.04 1.01 3.1e-01 -0.03 0.11 1.04 0.00
## Age 0.03 0.04 0.90 3.7e-01 -0.04 0.10 1.00 0.00
## HAMNat_total -0.36 0.04 -9.98 5.2e-22 -0.43 -0.29 1.04 0.13
##
## Residual Standard Error = 0.94 with 695 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.36 0.13 0.24 0.06 0.12 0.02 34.23 3 695 1.21e-20lm_HAMNat_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.03 0.04 0.73 4.7e-01 -0.04 0.10 1.05 0.00
## Age -0.02 0.04 -0.58 5.6e-01 -0.10 0.05 1.21 0.00
## GPA 0.14 0.04 3.44 6.2e-04 0.06 0.22 1.32 0.03
## HAMNat_total -0.32 0.04 -8.57 6.5e-17 -0.40 -0.25 1.15 0.11
##
## Residual Standard Error = 0.93 with 694 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.38 0.14 0.28 0.08 0.14 0.02 29.03 4 694 2.47e-22anova(lm_HAMNat_1_corr, lm_HAMNat_2a_corr, lm_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 696 695.2853 NA NA NA NA
## 2 695 661.2959 1 33.98944 39.44848 5.936816e-10
## 3 694 597.9616 1 63.33432 73.50642 6.502097e-17anova(lm_HAMNat_1_corr, lm_HAMNat_2b_corr, lm_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 696 695.2853 NA NA NA NA
## 2 695 608.1420 1 87.14333 101.13939 2.634196e-22
## 3 694 597.9616 1 10.18044 11.81551 6.224426e-04#Criterion: M1
#Correcting for range restriction
Cov_Mat_HAMNat_Incumbents_M1 <- cov((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, HAMNat_total, M1)), use = "complete.obs")
Cor_Mat_HAMNat_Incumbents_M1 <- cor((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, HAMNat_total, M1)), use = "complete.obs")
Cor_Mat_HAMNat_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_HAMNat_Incumbents_M1, vnp = Cov_Mat_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_Incumbents_Corr_M1) <- colnames(Cor_Mat_HAMNat_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'M1')
#Models
lm_HAMNat_1_corr_M1 <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_M1_1), plot = F)
lm_HAMNat_2a_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_M1_2a), plot = F)
lm_HAMNat_2b_corr_M1 <- lmCor(M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_M1_2b), plot = F)
lm_HAMNat_3_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_M1_3), plot = F)
#Results
lm_HAMNat_1_corr_M1## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.11 0.06 -1.77 0.0780 -0.24 0.01 1 0.01
## Age 0.19 0.06 3.03 0.0027 0.07 0.32 1 0.04
##
## Residual Standard Error = 0.98 with 230 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.22 0.05 0.22 0.05 0.04 0.03 6.06 2 230 0.00273lm_HAMNat_2a_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.12 0.06 -1.96 5.2e-02 -0.24 0.00 1.0 0.01
## Age 0.06 0.07 0.88 3.8e-01 -0.07 0.19 1.2 0.01
## GPA 0.33 0.07 4.97 1.3e-06 0.20 0.47 1.2 0.12
##
## Residual Standard Error = 0.93 with 229 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.38 0.14 0.34 0.12 0.13 0.04 12.7 3 229 1.04e-07lm_HAMNat_2b_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.02 0.06 -0.33 7.4e-01 -0.13 0.10 1.04 0.00
## Age 0.17 0.06 2.98 3.2e-03 0.06 0.28 1.00 0.03
## HAMNat_total -0.47 0.06 -8.12 2.9e-14 -0.59 -0.36 1.04 0.23
##
## Residual Standard Error = 0.86 with 229 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.51 0.26 0.42 0.18 0.25 0.05 27.16 3 229 4.59e-15lm_HAMNat_3_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.06 -0.59 5.5e-01 -0.15 0.08 1.05 0.00
## Age 0.09 0.06 1.48 1.4e-01 -0.03 0.21 1.21 0.02
## GPA 0.20 0.06 3.14 1.9e-03 0.07 0.33 1.32 0.07
## HAMNat_total -0.42 0.06 -6.96 3.5e-11 -0.53 -0.30 1.15 0.20
##
## Residual Standard Error = 0.85 with 228 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.54 0.29 0.47 0.22 0.28 0.05 23.62 4 228 2.35e-16anova(lm_HAMNat_1_corr_M1, lm_HAMNat_2a_corr_M1, lm_HAMNat_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 230 220.3920 NA NA NA NA
## 2 229 198.9016 1 21.49035 29.87233 1.202067e-07
## 3 228 164.0247 1 34.87697 48.48020 3.523297e-11anova(lm_HAMNat_1_corr_M1, lm_HAMNat_2b_corr_M1, lm_HAMNat_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 230 220.3920 NA NA NA NA
## 2 229 171.1166 1 49.275406 68.494527 1.052457e-14
## 3 228 164.0247 1 7.091912 9.858004 1.914482e-03#Criterion: PCGPA
#Models
lm_TMS_via_Uni_TMS_1 <- lm(PCGPA ~ Gender + Age, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_2b <- lm(PCGPA ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_3 <- lm(PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_TMS)
#Results
summary(lm_TMS_via_Uni_TMS_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73839 -0.44850 -0.08726 0.42088 1.84336
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.762038 0.130069 13.547 < 2e-16 ***
## Gender -0.156523 0.034104 -4.590 4.77e-06 ***
## Age 0.030618 0.006086 5.031 5.42e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6366 on 1670 degrees of freedom
## (12 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.02529, Adjusted R-squared: 0.02413
## F-statistic: 21.67 on 2 and 1670 DF, p-value: 5.122e-10summary(lm_TMS_via_Uni_TMS_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73009 -0.46048 -0.09778 0.42324 1.82665
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.885646 0.132996 14.178 < 2e-16 ***
## Gender -0.166507 0.034035 -4.892 1.09e-06 ***
## Age 0.012432 0.007532 1.650 0.099 .
## GPA 0.172177 0.042375 4.063 5.07e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6337 on 1669 degrees of freedom
## (12 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.03484, Adjusted R-squared: 0.03311
## F-statistic: 20.08 on 3 and 1669 DF, p-value: 8.692e-13summary(lm_TMS_via_Uni_TMS_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.54058 -0.43393 -0.09008 0.40992 1.89563
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.205643 0.267509 11.983 < 2e-16 ***
## Gender -0.137689 0.033872 -4.065 5.03e-05 ***
## Age 0.024263 0.006108 3.972 7.42e-05 ***
## TMS_total -0.012392 0.002013 -6.155 9.38e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6297 on 1669 degrees of freedom
## (12 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.04693, Adjusted R-squared: 0.04521
## F-statistic: 27.39 on 3 and 1669 DF, p-value: < 2.2e-16summary(lm_TMS_via_Uni_TMS_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5319 -0.4397 -0.0809 0.4133 1.8683
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.332620 0.268006 12.435 < 2e-16 ***
## Gender -0.147679 0.033797 -4.370 1.32e-05 ***
## Age 0.005984 0.007522 0.796 0.426
## GPA 0.172938 0.041908 4.127 3.86e-05 ***
## TMS_total -0.012416 0.002004 -6.197 7.25e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6267 on 1668 degrees of freedom
## (12 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.05656, Adjusted R-squared: 0.0543
## F-statistic: 25 on 4 and 1668 DF, p-value: < 2.2e-16anova(lm_TMS_via_Uni_TMS_1, lm_TMS_via_Uni_TMS_2a, lm_TMS_via_Uni_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1670 676.77
## 2 1669 670.14 1 6.6288 16.879 4.177e-05 ***
## 3 1668 655.06 1 15.0799 38.398 7.253e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_via_Uni_TMS_1, lm_TMS_via_Uni_TMS_2b, lm_TMS_via_Uni_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + TMS_total
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 1670 676.77
## 2 1669 661.75 1 15.0212 38.249 7.816e-10 ***
## 3 1668 655.06 1 6.6875 17.029 3.864e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_TMS_via_Uni_TMS_M1_1 <- lm(M1 ~ Gender + Age, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_M1_2b <- lm(M1 ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_TMS)
lm_TMS_via_Uni_TMS_M1_3 <- lm(M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_TMS)
#Results
summary(lm_TMS_via_Uni_TMS_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.58260 -0.52371 0.03519 0.53519 2.53519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.55919 0.37239 4.187 3.78e-05 ***
## Gender -0.21343 0.10256 -2.081 0.038330 *
## Age 0.05890 0.01741 3.384 0.000816 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7699 on 282 degrees of freedom
## (1400 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.05001, Adjusted R-squared: 0.04328
## F-statistic: 7.423 on 2 and 282 DF, p-value: 0.0007213summary(lm_TMS_via_Uni_TMS_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.64239 -0.54869 0.00469 0.50957 2.55325
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.71712 0.38320 4.481 1.08e-05 ***
## Gender -0.23163 0.10282 -2.253 0.0251 *
## Age 0.03398 0.02293 1.482 0.1395
## GPA 0.24279 0.14605 1.662 0.0976 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7675 on 281 degrees of freedom
## (1400 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.05927, Adjusted R-squared: 0.04922
## F-statistic: 5.901 on 3 and 281 DF, p-value: 0.0006435summary(lm_TMS_via_Uni_TMS_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73632 -0.57976 0.02786 0.54711 2.54016
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.787994 0.747109 5.070 7.22e-07 ***
## Gender -0.214313 0.100665 -2.129 0.034126 *
## Age 0.050813 0.017247 2.946 0.003486 **
## TMS_total -0.019253 0.005628 -3.421 0.000718 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7557 on 281 degrees of freedom
## (1400 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.08799, Adjusted R-squared: 0.07825
## F-statistic: 9.037 on 3 and 281 DF, p-value: 9.88e-06summary(lm_TMS_via_Uni_TMS_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.69157 -0.57428 0.01065 0.55980 2.55644
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.884559 0.747973 5.193 3.98e-07 ***
## Gender -0.230804 0.100998 -2.285 0.023047 *
## Age 0.028379 0.022583 1.257 0.209933
## GPA 0.220251 0.143615 1.534 0.126253
## TMS_total -0.018849 0.005621 -3.353 0.000909 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7539 on 280 degrees of freedom
## (1400 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.09559, Adjusted R-squared: 0.08267
## F-statistic: 7.398 on 4 and 280 DF, p-value: 1.12e-05anova(lm_TMS_via_Uni_TMS_M1_1, lm_TMS_via_Uni_TMS_M1_2a, lm_TMS_via_Uni_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 282 167.17
## 2 281 165.54 1 1.6280 2.8642 0.0916812 .
## 3 280 159.15 1 6.3912 11.2445 0.0009087 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_via_Uni_TMS_M1_1, lm_TMS_via_Uni_TMS_M1_2b, lm_TMS_via_Uni_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + TMS_total
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 282 167.17
## 2 281 160.49 1 6.6824 11.757 0.0006974 ***
## 3 280 159.15 1 1.3368 2.352 0.1262531
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Models
lm_HAMNat_via_Uni_TMS_1 <- lm(PCGPA ~ Gender + Age, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_2b <- lm(PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_3 <- lm(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
#Results
summary(lm_HAMNat_via_Uni_TMS_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2550 -0.4541 -0.1540 0.4451 1.7956
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3024791 0.2762951 8.333 1.36e-15 ***
## Gender -0.0505769 0.0678616 -0.745 0.457
## Age 0.0001109 0.0124167 0.009 0.993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.622 on 390 degrees of freedom
## (5 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.001423, Adjusted R-squared: -0.003698
## F-statistic: 0.2779 on 2 and 390 DF, p-value: 0.7575summary(lm_HAMNat_via_Uni_TMS_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2843 -0.4289 -0.1194 0.4073 1.7973
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.36504 0.27734 8.528 3.36e-16 ***
## Gender -0.06276 0.06794 -0.924 0.3562
## Age -0.01491 0.01469 -1.015 0.3107
## GPA 0.16311 0.08590 1.899 0.0583 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.62 on 389 degrees of freedom
## (5 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.01059, Adjusted R-squared: 0.002964
## F-statistic: 1.388 on 3 and 389 DF, p-value: 0.2459summary(lm_HAMNat_via_Uni_TMS_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.26239 -0.38399 -0.08203 0.42704 1.69706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.470803 0.265799 9.296 < 2e-16 ***
## Gender 0.015795 0.065839 0.240 0.811
## Age -0.008218 0.011959 -0.687 0.492
## HAMNat_total -0.221479 0.036399 -6.085 2.79e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5951 on 389 degrees of freedom
## (5 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.08821, Adjusted R-squared: 0.08118
## F-statistic: 12.54 on 3 and 389 DF, p-value: 7.608e-08summary(lm_HAMNat_via_Uni_TMS_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.24281 -0.40017 -0.08544 0.43064 1.66126
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.516118 0.266986 9.424 < 2e-16 ***
## Gender 0.005111 0.066095 0.077 0.938
## Age -0.019698 0.014097 -1.397 0.163
## GPA 0.126388 0.082549 1.531 0.127
## HAMNat_total -0.217318 0.036437 -5.964 5.54e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5941 on 388 degrees of freedom
## (5 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.09368, Adjusted R-squared: 0.08434
## F-statistic: 10.03 on 4 and 388 DF, p-value: 9.885e-08anova(lm_HAMNat_via_Uni_TMS_1, lm_HAMNat_via_Uni_TMS_2a, lm_HAMNat_via_Uni_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 390 150.90
## 2 389 149.51 1 1.3859 3.9263 0.04824 *
## 3 388 136.96 1 12.5559 35.5712 5.538e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_via_Uni_TMS_1, lm_HAMNat_via_Uni_TMS_2b, lm_HAMNat_via_Uni_TMS_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + HAMNat_total
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 390 150.90
## 2 389 137.78 1 13.1144 37.1533 2.637e-09 ***
## 3 388 136.96 1 0.8275 2.3442 0.1266
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_HAMNat_via_Uni_TMS_M1_1 <- lm(M1 ~ Gender + Age, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_M1_2b <- lm(M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
lm_HAMNat_via_Uni_TMS_M1_3 <- lm(M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
#Results
summary(lm_HAMNat_via_Uni_TMS_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52784 -0.58526 -0.02784 0.52332 1.59691
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.53031 0.65077 2.352 0.0205 *
## Gender -0.12475 0.16339 -0.764 0.4468
## Age 0.05907 0.03092 1.910 0.0588 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7728 on 107 degrees of freedom
## (288 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.0346, Adjusted R-squared: 0.01655
## F-statistic: 1.917 on 2 and 107 DF, p-value: 0.152summary(lm_HAMNat_via_Uni_TMS_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.50919 -0.57744 -0.02765 0.50797 1.62727
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.51132 0.66119 2.286 0.0243 *
## Gender -0.11930 0.16658 -0.716 0.4755
## Age 0.06309 0.03749 1.683 0.0954 .
## GPA -0.04292 0.22403 -0.192 0.8484
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7763 on 106 degrees of freedom
## (288 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.03493, Adjusted R-squared: 0.007619
## F-statistic: 1.279 on 3 and 106 DF, p-value: 0.2854summary(lm_HAMNat_via_Uni_TMS_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.64689 -0.44191 -0.03986 0.55008 1.82072
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.41976 0.62008 3.902 0.000168 ***
## Gender -0.05152 0.14942 -0.345 0.730921
## Age 0.02191 0.02917 0.751 0.454086
## HAMNat_total -0.41707 0.08644 -4.825 4.72e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7031 on 106 degrees of freedom
## (288 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2084, Adjusted R-squared: 0.186
## F-statistic: 9.304 on 3 and 106 DF, p-value: 1.626e-05summary(lm_HAMNat_via_Uni_TMS_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_TMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.65110 -0.44741 -0.03945 0.55857 1.79808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.43658 0.63170 3.857 0.000198 ***
## Gender -0.05550 0.15215 -0.365 0.715994
## Age 0.01874 0.03534 0.530 0.596993
## GPA 0.03282 0.20444 0.161 0.872777
## HAMNat_total -0.41815 0.08710 -4.801 5.26e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7063 on 105 degrees of freedom
## (288 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2086, Adjusted R-squared: 0.1785
## F-statistic: 6.921 on 4 and 105 DF, p-value: 5.523e-05anova(lm_HAMNat_via_Uni_TMS_M1_1, lm_HAMNat_via_Uni_TMS_M1_2a, lm_HAMNat_via_Uni_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 107 63.901
## 2 106 63.879 1 0.0221 0.0443 0.8336
## 3 105 52.381 1 11.4978 23.0478 5.263e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_via_Uni_TMS_M1_1, lm_HAMNat_via_Uni_TMS_M1_2b, lm_HAMNat_via_Uni_TMS_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + HAMNat_total
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 107 63.901
## 2 106 52.394 1 11.5070 23.0663 5.221e-06 ***
## 3 105 52.381 1 0.0129 0.0258 0.8728
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Correcting for range restriction
data_TMS_via_Uni_TMS$Gender <- as.numeric(data_TMS_via_Uni_TMS$Gender)
Cov_Mat_TMS_via_Uni_TMS_Incumbents <- cov((dplyr::select(data_TMS_via_Uni_TMS, Gender, Age, GPA, TMS_total, PCGPA)), use = "complete.obs")
Cov_Mat_TMS_via_Uni_TMS_Testtakers <- cov((dplyr::select(data_TMS_Testtakers, Gender, Age, GPA, TMS_total)))
Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_TMS_via_Uni_TMS_Incumbents, vnp = Cov_Mat_TMS_via_Uni_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr) <- colnames(Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'PCGPA')
#Models
lm_TMS_via_Uni_TMS_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_TMS_1), plot = F)
lm_TMS_via_Uni_TMS_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_TMS_2a), plot = F)
lm_TMS_via_Uni_TMS_2b_corr <- lmCor(PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_TMS_2b), plot = F)
lm_TMS_via_Uni_TMS_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_TMS_3), plot = F)
#Results
lm_TMS_via_Uni_TMS_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.12 0.02 -4.80 1.8e-06 -0.16 -0.07 1 0.01
## Age 0.11 0.02 4.57 5.3e-06 0.06 0.16 1 0.01
##
## Residual Standard Error = 0.99 with 1670 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.16 0.02 0.16 0.02 0.02 0.01 20.85 2 1670 1.14e-09lm_TMS_via_Uni_TMS_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.12 0.02 -4.92 9.7e-07 -0.16 -0.07 1.00 0.01
## Age 0.03 0.03 1.22 2.2e-01 -0.02 0.09 1.27 0.00
## GPA 0.17 0.03 6.27 4.6e-10 0.12 0.22 1.27 0.03
##
## Residual Standard Error = 0.98 with 1669 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.22 0.05 0.2 0.04 0.05 0.01 27.33 3 1669 2.98e-17lm_TMS_via_Uni_TMS_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.10 0.02 -4.05 5.3e-05 -0.14 -0.05 1.01 0.01
## Age 0.07 0.02 3.08 2.1e-03 0.03 0.12 1.04 0.01
## TMS_total -0.21 0.02 -8.50 4.3e-17 -0.25 -0.16 1.04 0.05
##
## Residual Standard Error = 0.97 with 1669 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.25 0.06 0.24 0.06 0.06 0.01 38.55 3 1669 4.38e-24lm_TMS_via_Uni_TMS_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.10 0.02 -4.23 2.5e-05 -0.15 -0.05 1.01 0.01
## Age 0.02 0.03 0.82 4.1e-01 -0.03 0.07 1.28 0.00
## GPA 0.12 0.03 4.55 5.6e-06 0.07 0.18 1.34 0.02
## TMS_total -0.18 0.02 -7.29 4.6e-13 -0.23 -0.13 1.10 0.04
##
## Residual Standard Error = 0.96 with 1668 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.28 0.08 0.26 0.07 0.07 0.01 34.44 4 1668 1.17e-27anova(lm_TMS_via_Uni_TMS_1_corr, lm_TMS_via_Uni_TMS_2a_corr, lm_TMS_via_Uni_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 1670 1631.264 NA NA NA NA
## 2 1669 1593.710 1 37.55367 40.55800 2.461458e-10
## 3 1668 1544.443 1 49.26758 53.20905 4.614908e-13anova(lm_TMS_via_Uni_TMS_1_corr, lm_TMS_via_Uni_TMS_2b_corr, lm_TMS_via_Uni_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 1670 1631.264 NA NA NA NA
## 2 1669 1563.650 1 67.61384 73.02303 2.844690e-17
## 3 1668 1544.443 1 19.20741 20.74403 5.630356e-06#Criterion: M1
#Correcting for range restriction
Cov_Mat_TMS_via_Uni_TMS_Incumbents_M1 <- cov((dplyr::select(data_TMS_via_Uni_TMS, Gender, Age, GPA, TMS_total, M1)), use = "complete.obs")
Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_TMS_via_Uni_TMS_Incumbents_M1, vnp = Cov_Mat_TMS_via_Uni_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1) <- colnames(Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'M1')
#Models
lm_TMS_via_Uni_TMS_M1_1_corr <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_TMS_M1_1), plot = F)
lm_TMS_via_Uni_TMS_M1_2a_corr <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2a), plot = F)
lm_TMS_via_Uni_TMS_M1_2b_corr <- lmCor(M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2b), plot = F)
lm_TMS_via_Uni_TMS_M1_3_corr <- lmCor(M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_TMS_M1_3), plot = F)
#Results
lm_TMS_via_Uni_TMS_M1_1_corr## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.15 0.06 -2.54 0.0120 -0.26 -0.03 1 0.02
## Age 0.18 0.06 3.14 0.0019 0.07 0.30 1 0.03
##
## Residual Standard Error = 0.98 with 282 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.23 0.05 0.23 0.05 0.05 0.03 7.76 2 282 0.000522lm_TMS_via_Uni_TMS_M1_2a_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.15 0.06 -2.60 0.0098 -0.26 -0.04 1.00 0.02
## Age 0.10 0.06 1.51 0.1300 -0.03 0.22 1.27 0.02
## GPA 0.18 0.06 2.85 0.0046 0.06 0.31 1.27 0.04
##
## Residual Standard Error = 0.96 with 281 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.28 0.08 0.28 0.08 0.07 0.03 8.02 3 281 3.8e-05lm_TMS_via_Uni_TMS_M1_2b_corr## Call: lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.12 0.06 -2.19 3.0e-02 -0.24 -0.01 1.01 0.02
## Age 0.14 0.06 2.42 1.6e-02 0.03 0.25 1.04 0.02
## TMS_total -0.25 0.06 -4.33 2.1e-05 -0.36 -0.14 1.04 0.07
##
## Residual Standard Error = 0.95 with 281 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.33 0.11 0.32 0.1 0.1 0.03 11.76 3 281 2.79e-07lm_TMS_via_Uni_TMS_M1_3_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.13 0.06 -2.26 0.02400 -0.24 -0.02 1.01 0.02
## Age 0.08 0.06 1.33 0.19000 -0.04 0.21 1.28 0.01
## GPA 0.13 0.06 1.99 0.04800 0.00 0.26 1.34 0.03
## TMS_total -0.22 0.06 -3.79 0.00018 -0.34 -0.11 1.10 0.06
##
## Residual Standard Error = 0.94 with 280 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.35 0.12 0.34 0.12 0.11 0.04 9.9 4 280 1.66e-07anova(lm_TMS_via_Uni_TMS_M1_1_corr, lm_TMS_via_Uni_TMS_M1_2a_corr, lm_TMS_via_Uni_TMS_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 282 269.1772 NA NA NA NA
## 2 281 261.5984 1 7.578805 8.528861 0.0037789560
## 3 280 248.8099 1 12.788416 14.391533 0.0001819423anova(lm_TMS_via_Uni_TMS_M1_1_corr, lm_TMS_via_Uni_TMS_M1_2b_corr, lm_TMS_via_Uni_TMS_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 282 269.1772 NA NA NA NA
## 2 281 252.3189 1 16.858217 18.971513 1.861425e-05
## 3 280 248.8099 1 3.509003 3.948881 4.787676e-02#Criterion: PCGPA
#Correcting for range restriction
Cov_Mat_HAMNat_via_Uni_TMS_Incumbents <- cov((dplyr::select(data_HAMNat_via_Uni_TMS, Gender, Age, GPA, HAMNat_total, PCGPA)), use = "complete.obs")
Cov_Mat_HAMNat_via_Uni_TMS_Testtakers <- cov((dplyr::select(data_HAMNat_Testtakers, Gender, Age, GPA, HAMNat_total)))
Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_HAMNat_via_Uni_TMS_Incumbents, vnp = Cov_Mat_HAMNat_via_Uni_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr) <- colnames(Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'PCGPA')
#Models
lm_HAMNat_via_Uni_TMS_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_TMS_1), plot = F)
lm_HAMNat_via_Uni_TMS_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_TMS_2a), plot = F)
lm_HAMNat_via_Uni_TMS_2b_corr <- lmCor(PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_TMS_2b), plot = F)
lm_HAMNat_via_Uni_TMS_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_TMS_3), plot = F)
#Results
lm_HAMNat_via_Uni_TMS_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.05 0.05 -1.09 0.28 -0.15 0.04 1 0
## Age -0.03 0.05 -0.53 0.59 -0.13 0.07 1 0
##
## Residual Standard Error = 1 with 390 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.06 0 0.06 0 0 0.01 0.74 2 390 0.475lm_HAMNat_via_Uni_TMS_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.06 0.05 -1.17 0.24000 -0.16 0.04 1.0 0.00
## Age -0.11 0.05 -1.93 0.05500 -0.21 0.00 1.2 0.00
## GPA 0.19 0.05 3.51 0.00049 0.08 0.30 1.2 0.03
##
## Residual Standard Error = 0.99 with 389 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.19 0.03 0.16 0.02 0.03 0.02 4.63 3 389 0.0034lm_HAMNat_via_Uni_TMS_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.01 0.05 0.22 8.2e-01 -0.09 0.11 1.04 0.00
## Age -0.04 0.05 -0.93 3.5e-01 -0.14 0.05 1.00 0.00
## HAMNat_total -0.33 0.05 -6.67 8.6e-11 -0.42 -0.23 1.04 0.11
##
## Residual Standard Error = 0.95 with 389 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.33 0.11 0.22 0.05 0.1 0.03 15.39 3 389 1.75e-09lm_HAMNat_via_Uni_TMS_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.00 0.05 0.08 9.4e-01 -0.09 0.10 1.05 0.00
## Age -0.08 0.05 -1.57 1.2e-01 -0.19 0.02 1.21 0.00
## GPA 0.10 0.05 1.75 8.2e-02 -0.01 0.20 1.32 0.01
## HAMNat_total -0.30 0.05 -5.86 9.6e-09 -0.40 -0.20 1.15 0.10
##
## Residual Standard Error = 0.95 with 388 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.34 0.11 0.28 0.08 0.1 0.03 12.37 4 388 1.77e-09anova(lm_HAMNat_via_Uni_TMS_1_corr, lm_HAMNat_via_Uni_TMS_2a_corr, lm_HAMNat_via_Uni_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 390 390.5081 NA NA NA NA
## 2 389 378.4883 1 12.01986 13.41433 2.842646e-04
## 3 388 347.6659 1 30.82233 34.39814 9.624090e-09anova(lm_HAMNat_via_Uni_TMS_1_corr, lm_HAMNat_via_Uni_TMS_2b_corr, lm_HAMNat_via_Uni_TMS_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 390 390.5081 NA NA NA NA
## 2 389 350.3985 1 40.109650 44.76293 7.767538e-11
## 3 388 347.6659 1 2.732538 3.04955 8.155091e-02#Criterion: M1
#Correcting for range restriction
Cov_Mat_HAMNat_via_Uni_TMS_Incumbents_M1 <- cov((dplyr::select(data_HAMNat_via_Uni_TMS, Gender, Age, GPA, HAMNat_total, M1)), use = "complete.obs")
Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_HAMNat_via_Uni_TMS_Incumbents_M1, vnp = Cov_Mat_HAMNat_via_Uni_TMS_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1) <- colnames(Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'M1')
#Models
lm_HAMNat_via_Uni_TMS_1_corr_M1 <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_1), plot = F)
lm_HAMNat_via_Uni_TMS_2a_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2a), plot = F)
lm_HAMNat_via_Uni_TMS_2b_corr_M1 <- lmCor(M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2b), plot = F)
lm_HAMNat_via_Uni_TMS_3_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_3), plot = F)
#Results
lm_HAMNat_via_Uni_TMS_1_corr_M1## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.12 0.1 -1.3 0.20 -0.31 0.07 1 0.02
## Age 0.10 0.1 1.0 0.32 -0.09 0.28 1 0.01
##
## Residual Standard Error = 1 with 107 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.15 0.02 0.15 0.02 0.01 0.03 1.32 2 107 0.272lm_HAMNat_via_Uni_TMS_2a_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.13 0.09 -1.34 0.18 -0.32 0.06 1.0 0.02
## Age 0.03 0.10 0.26 0.79 -0.18 0.23 1.2 0.00
## GPA 0.17 0.10 1.60 0.11 -0.04 0.37 1.2 0.03
##
## Residual Standard Error = 0.99 with 106 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.22 0.05 0.2 0.04 0.02 0.04 1.75 3 106 0.162lm_HAMNat_via_Uni_TMS_2b_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.09 -0.35 7.2e-01 -0.20 0.14 1.04 0.00
## Age 0.07 0.09 0.82 4.1e-01 -0.10 0.24 1.00 0.01
## HAMNat_total -0.46 0.09 -5.33 5.5e-07 -0.64 -0.29 1.04 0.22
##
## Residual Standard Error = 0.89 with 106 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.48 0.23 0.37 0.14 0.21 0.07 10.58 3 106 3.84e-06lm_HAMNat_via_Uni_TMS_3_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.09 -0.37 7.1e-01 -0.21 0.14 1.05 0.00
## Age 0.06 0.09 0.66 5.1e-01 -0.12 0.25 1.21 0.01
## GPA 0.02 0.10 0.20 8.4e-01 -0.18 0.21 1.32 0.00
## HAMNat_total -0.46 0.09 -5.01 2.3e-06 -0.64 -0.28 1.15 0.22
##
## Residual Standard Error = 0.89 with 105 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.48 0.23 0.36 0.13 0.2 0.07 7.87 4 105 1.38e-05anova(lm_HAMNat_via_Uni_TMS_1_corr_M1, lm_HAMNat_via_Uni_TMS_2a_corr_M1, lm_HAMNat_via_Uni_TMS_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 107 106.38307 NA NA NA NA
## 2 106 103.86659 1 2.516483 3.151002 7.875063e-02
## 3 105 83.85612 1 20.010471 25.056007 2.253669e-06anova(lm_HAMNat_via_Uni_TMS_1_corr_M1, lm_HAMNat_via_Uni_TMS_2b_corr_M1, lm_HAMNat_via_Uni_TMS_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_TMS_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_TMS_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 107 106.38307 NA NA NA NA
## 2 106 83.88842 1 22.49464703 28.16655555 6.155523e-07
## 3 105 83.85612 1 0.03230735 0.04045348 8.409856e-01#Criterion: PCGPA
#Models
lm_TMS_via_Uni_HAMNat_1 <- lm(PCGPA ~ Gender + Age, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_2b <- lm(PCGPA ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_3 <- lm(PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_HAMNat)
#Results
summary(lm_TMS_via_Uni_HAMNat_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.09056 -0.42816 -0.03642 0.41498 1.61224
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.84004 0.47109 1.783 0.0762 .
## Gender 0.05960 0.09339 0.638 0.5242
## Age 0.05413 0.02173 2.491 0.0136 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6011 on 184 degrees of freedom
## (1 Beobachtung als fehlend gelöscht)
## Multiple R-squared: 0.03431, Adjusted R-squared: 0.02381
## F-statistic: 3.268 on 2 and 184 DF, p-value: 0.04029summary(lm_TMS_via_Uni_HAMNat_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.09581 -0.42123 -0.02465 0.34629 1.68554
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.98375 0.46809 2.102 0.0370 *
## Gender 0.02063 0.09341 0.221 0.8255
## Age 0.02200 0.02500 0.880 0.3801
## GPA 0.36270 0.14530 2.496 0.0134 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5927 on 183 degrees of freedom
## (1 Beobachtung als fehlend gelöscht)
## Multiple R-squared: 0.06611, Adjusted R-squared: 0.0508
## F-statistic: 4.318 on 3 and 183 DF, p-value: 0.005719summary(lm_TMS_via_Uni_HAMNat_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2010 -0.4036 -0.0605 0.3799 1.6164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.110315 0.733182 5.606 7.52e-08 ***
## Gender 0.037853 0.086718 0.437 0.6630
## Age 0.039653 0.020326 1.951 0.0526 .
## TMS_total -0.028698 0.005166 -5.555 9.68e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5575 on 183 degrees of freedom
## (1 Beobachtung als fehlend gelöscht)
## Multiple R-squared: 0.1736, Adjusted R-squared: 0.1601
## F-statistic: 12.82 on 3 and 183 DF, p-value: 1.221e-07summary(lm_TMS_via_Uni_HAMNat_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.28576 -0.36704 -0.06162 0.37344 1.67711
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.120534 0.725472 5.680 5.26e-08 ***
## Gender 0.006239 0.086981 0.072 0.9429
## Age 0.013469 0.023321 0.578 0.5643
## GPA 0.300977 0.135725 2.218 0.0278 *
## TMS_total -0.027741 0.005130 -5.407 1.99e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5516 on 182 degrees of freedom
## (1 Beobachtung als fehlend gelöscht)
## Multiple R-squared: 0.1954, Adjusted R-squared: 0.1777
## F-statistic: 11.05 on 4 and 182 DF, p-value: 4.814e-08anova(lm_TMS_via_Uni_HAMNat_1, lm_TMS_via_Uni_HAMNat_2a, lm_TMS_via_Uni_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 184 66.473
## 2 183 64.284 1 2.1887 7.1923 0.007995 **
## 3 182 55.385 1 8.8984 29.2408 1.99e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_via_Uni_HAMNat_1, lm_TMS_via_Uni_HAMNat_2b, lm_TMS_via_Uni_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + TMS_total
## Model 3: PCGPA ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 184 66.473
## 2 183 56.882 1 9.5907 31.5156 7.285e-08 ***
## 3 182 55.385 1 1.4965 4.9176 0.02782 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_TMS_via_Uni_HAMNat_M1_1 <- lm(M1 ~ Gender + Age, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_M1_2b <- lm(M1 ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_HAMNat)
lm_TMS_via_Uni_HAMNat_M1_3 <- lm(M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_HAMNat)
#Results
summary(lm_TMS_via_Uni_HAMNat_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2000 -0.6243 -0.1327 0.5353 1.9009
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.63672 1.06093 1.543 0.127
## Gender -0.17644 0.17835 -0.989 0.325
## Age 0.03362 0.05046 0.666 0.507
##
## Residual standard error: 0.8079 on 87 degrees of freedom
## (98 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.0172, Adjusted R-squared: -0.005389
## F-statistic: 0.7615 on 2 and 87 DF, p-value: 0.4701summary(lm_TMS_via_Uni_HAMNat_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3935 -0.5479 -0.1230 0.5903 1.7032
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.28653 1.02461 2.232 0.02824 *
## Gender -0.23951 0.17011 -1.408 0.16273
## Age -0.06827 0.05694 -1.199 0.23389
## GPA 0.96678 0.29331 3.296 0.00143 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7657 on 86 degrees of freedom
## (98 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1274, Adjusted R-squared: 0.097
## F-statistic: 4.187 on 3 and 86 DF, p-value: 0.008136summary(lm_TMS_via_Uni_HAMNat_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + TMS_total, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.2960 -0.5144 -0.1583 0.4463 2.2768
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.51125 1.53645 3.587 0.000555 ***
## Gender -0.23833 0.16984 -1.403 0.164135
## Age 0.03023 0.04778 0.633 0.528642
## TMS_total -0.03618 0.01086 -3.332 0.001273 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7647 on 86 degrees of freedom
## (98 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1296, Adjusted R-squared: 0.09921
## F-statistic: 4.267 on 3 and 86 DF, p-value: 0.007375summary(lm_TMS_via_Uni_HAMNat_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + TMS_total, data = data_TMS_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.51955 -0.51295 -0.08223 0.51851 1.97485
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.70229 1.46705 3.887 0.000201 ***
## Gender -0.28863 0.16284 -1.772 0.079898 .
## Age -0.06080 0.05431 -1.119 0.266119
## GPA 0.86692 0.28129 3.082 0.002772 **
## TMS_total -0.03252 0.01043 -3.119 0.002476 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7295 on 85 degrees of freedom
## (98 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2171, Adjusted R-squared: 0.1802
## F-statistic: 5.891 on 4 and 85 DF, p-value: 0.0003113anova(lm_TMS_via_Uni_HAMNat_M1_1, lm_TMS_via_Uni_HAMNat_M1_2a, lm_TMS_via_Uni_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 87 56.786
## 2 86 50.417 1 6.3694 11.9675 0.0008487 ***
## 3 85 45.239 1 5.1784 9.7297 0.0024757 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_TMS_via_Uni_HAMNat_M1_1, lm_TMS_via_Uni_HAMNat_M1_2b, lm_TMS_via_Uni_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + TMS_total
## Model 3: M1 ~ Gender + Age + GPA + TMS_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 87 56.786
## 2 86 50.294 1 6.4925 12.1990 0.0007614 ***
## 3 85 45.239 1 5.0552 9.4982 0.0027721 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Models
lm_HAMNat_via_Uni_HAMNat_1 <- lm(PCGPA ~ Gender + Age, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_2a <- lm(PCGPA ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_2b <- lm(PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_3 <- lm(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
#Results
summary(lm_HAMNat_via_Uni_HAMNat_1)##
## Call:
## lm(formula = PCGPA ~ Gender + Age, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.07981 -0.49224 -0.04001 0.41309 1.74343
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.14765 0.30742 3.733 0.000226 ***
## Gender 0.01657 0.07281 0.228 0.820170
## Age 0.03981 0.01373 2.900 0.004000 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6271 on 303 degrees of freedom
## (2 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.02738, Adjusted R-squared: 0.02096
## F-statistic: 4.265 on 2 and 303 DF, p-value: 0.0149summary(lm_HAMNat_via_Uni_HAMNat_2a)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.10586 -0.49603 -0.02802 0.38929 1.74969
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.261594 0.308875 4.084 5.66e-05 ***
## Gender -0.001021 0.072643 -0.014 0.9888
## Age 0.017634 0.016527 1.067 0.2868
## GPA 0.241237 0.101809 2.370 0.0184 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6223 on 302 degrees of freedom
## (2 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.04514, Adjusted R-squared: 0.03565
## F-statistic: 4.758 on 3 and 302 DF, p-value: 0.002945summary(lm_HAMNat_via_Uni_HAMNat_2b)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.14716 -0.42383 -0.04039 0.37439 1.73792
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.53315 0.29774 5.149 4.72e-07 ***
## Gender 0.09420 0.07007 1.344 0.17983
## Age 0.03522 0.01301 2.708 0.00716 **
## HAMNat_total -0.30056 0.04971 -6.046 4.38e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5932 on 302 degrees of freedom
## (2 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1324, Adjusted R-squared: 0.1238
## F-statistic: 15.36 on 3 and 302 DF, p-value: 2.509e-09summary(lm_HAMNat_via_Uni_HAMNat_3)##
## Call:
## lm(formula = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.23971 -0.42027 -0.03878 0.38264 1.78929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.69065 0.29804 5.673 3.30e-08 ***
## Gender 0.07612 0.06935 1.098 0.27327
## Age 0.00777 0.01561 0.498 0.61909
## GPA 0.29639 0.09609 3.084 0.00223 **
## HAMNat_total -0.31421 0.04923 -6.383 6.55e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.585 on 301 degrees of freedom
## (2 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.159, Adjusted R-squared: 0.1478
## F-statistic: 14.22 on 4 and 301 DF, p-value: 1.203e-10anova(lm_HAMNat_via_Uni_HAMNat_1, lm_HAMNat_via_Uni_HAMNat_2a, lm_HAMNat_via_Uni_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + GPA
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 303 119.14
## 2 302 116.97 1 2.1746 6.3534 0.01223 *
## 3 301 103.02 1 13.9450 40.7434 6.554e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_via_Uni_HAMNat_1, lm_HAMNat_via_Uni_HAMNat_2b, lm_HAMNat_via_Uni_HAMNat_3)## Analysis of Variance Table
##
## Model 1: PCGPA ~ Gender + Age
## Model 2: PCGPA ~ Gender + Age + HAMNat_total
## Model 3: PCGPA ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 303 119.14
## 2 302 106.28 1 12.864 37.5836 2.744e-09 ***
## 3 301 103.02 1 3.256 9.5132 0.002229 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: M1
#Models
lm_HAMNat_via_Uni_HAMNat_M1_1 <- lm(M1 ~ Gender + Age, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_M1_2a <- lm(M1 ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_M1_2b <- lm(M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
lm_HAMNat_via_Uni_HAMNat_M1_3 <- lm(M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
#Results
summary(lm_HAMNat_via_Uni_HAMNat_M1_1)##
## Call:
## lm(formula = M1 ~ Gender + Age, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.48678 -0.62509 -0.00642 0.39454 2.18573
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.05938 0.55117 0.108 0.91439
## Gender -0.07050 0.13594 -0.519 0.60497
## Age 0.09607 0.02430 3.954 0.00013 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7516 on 120 degrees of freedom
## (185 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1165, Adjusted R-squared: 0.1018
## F-statistic: 7.912 on 2 and 120 DF, p-value: 0.0005922summary(lm_HAMNat_via_Uni_HAMNat_M1_2a)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.47193 -0.53803 -0.05577 0.44008 2.01823
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.31661 0.53930 0.587 0.55827
## Gender -0.08715 0.13151 -0.663 0.50880
## Age 0.04365 0.02903 1.503 0.13538
## GPA 0.55382 0.18028 3.072 0.00264 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7265 on 119 degrees of freedom
## (185 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1814, Adjusted R-squared: 0.1608
## F-statistic: 8.791 on 3 and 119 DF, p-value: 2.597e-05summary(lm_HAMNat_via_Uni_HAMNat_M1_2b)##
## Call:
## lm(formula = M1 ~ Gender + Age + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.27308 -0.55401 -0.04016 0.36458 2.32167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.32829 0.54390 0.604 0.547263
## Gender 0.02028 0.13591 0.149 0.881650
## Age 0.09422 0.02362 3.989 0.000115 ***
## HAMNat_total -0.26700 0.09395 -2.842 0.005277 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7304 on 119 degrees of freedom
## (185 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.1727, Adjusted R-squared: 0.1518
## F-statistic: 8.278 on 3 and 119 DF, p-value: 4.783e-05summary(lm_HAMNat_via_Uni_HAMNat_M1_3)##
## Call:
## lm(formula = M1 ~ Gender + Age + GPA + HAMNat_total, data = data_HAMNat_via_Uni_HAMNat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.33258 -0.51398 -0.03666 0.40665 2.13699
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5586364 0.5319959 1.050 0.29583
## Gender -0.0005735 0.1317270 -0.004 0.99653
## Age 0.0443696 0.0282510 1.571 0.11897
## GPA 0.5277289 0.1756817 3.004 0.00326 **
## HAMNat_total -0.2523350 0.0910616 -2.771 0.00649 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.707 on 118 degrees of freedom
## (185 Beobachtungen als fehlend gelöscht)
## Multiple R-squared: 0.2314, Adjusted R-squared: 0.2054
## F-statistic: 8.883 on 4 and 118 DF, p-value: 2.639e-06anova(lm_HAMNat_via_Uni_HAMNat_M1_1, lm_HAMNat_via_Uni_HAMNat_M1_2a, lm_HAMNat_via_Uni_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + GPA
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 120 67.793
## 2 119 62.812 1 4.9810 9.9663 0.002024 **
## 3 118 58.974 1 3.8376 7.6786 0.006494 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(lm_HAMNat_via_Uni_HAMNat_M1_1, lm_HAMNat_via_Uni_HAMNat_M1_2b, lm_HAMNat_via_Uni_HAMNat_M1_3)## Analysis of Variance Table
##
## Model 1: M1 ~ Gender + Age
## Model 2: M1 ~ Gender + Age + HAMNat_total
## Model 3: M1 ~ Gender + Age + GPA + HAMNat_total
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 120 67.793
## 2 119 63.484 1 4.3089 8.6216 0.003995 **
## 3 118 58.974 1 4.5097 9.0234 0.003255 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Criterion: PCGPA
#Correcting for range restriction
data_TMS_via_Uni_HAMNat$Gender <- as.numeric(data_TMS_via_Uni_HAMNat$Gender)
Cov_Mat_TMS_via_Uni_HAMNat_Incumbents <- cov((dplyr::select(data_TMS_via_Uni_HAMNat, Gender, Age, GPA, TMS_total, PCGPA)), use = "complete.obs")
Cov_Mat_TMS_via_Uni_HAMNat_Testtakers <- cov((dplyr::select(data_TMS_Testtakers, Gender, Age, GPA, TMS_total)))
Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_TMS_via_Uni_HAMNat_Incumbents, vnp = Cov_Mat_TMS_via_Uni_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr) <- colnames(Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'PCGPA')
#Models
lm_TMS_via_Uni_HAMNat_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_HAMNat_1), plot = F)
lm_TMS_via_Uni_HAMNat_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_HAMNat_2a), plot = F)
lm_TMS_via_Uni_HAMNat_2b_corr <- lmCor(PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_HAMNat_2b), plot = F)
lm_TMS_via_Uni_HAMNat_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_TMS_via_Uni_HAMNat_3), plot = F)
#Results
lm_TMS_via_Uni_HAMNat_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.07 -0.45 0.6500 -0.17 0.11 1 0.00
## Age 0.22 0.07 3.08 0.0024 0.08 0.36 1 0.05
##
## Residual Standard Error = 0.98 with 184 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.22 0.05 0.18 0.03 0.04 0.03 4.8 2 184 0.00932lm_TMS_via_Uni_HAMNat_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.04 0.07 -0.51 6.1e-01 -0.17 0.10 1.00 0.00
## Age 0.07 0.08 0.96 3.4e-01 -0.08 0.23 1.27 0.02
## GPA 0.32 0.08 4.12 5.8e-05 0.17 0.47 1.27 0.11
##
## Residual Standard Error = 0.94 with 183 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.36 0.13 0.31 0.09 0.12 0.04 9.13 3 183 1.17e-05lm_TMS_via_Uni_HAMNat_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.01 0.06 0.16 8.7e-01 -0.12 0.14 1.01 0.00
## Age 0.14 0.07 2.17 3.1e-02 0.01 0.27 1.04 0.03
## TMS_total -0.45 0.07 -6.89 8.9e-11 -0.58 -0.32 1.04 0.21
##
## Residual Standard Error = 0.88 with 183 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.5 0.25 0.39 0.15 0.23 0.05 19.81 3 183 3.63e-11lm_TMS_via_Uni_HAMNat_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.00 0.06 0.07 9.5e-01 -0.12 0.13 1.01 0.00
## Age 0.05 0.07 0.70 4.9e-01 -0.09 0.19 1.28 0.01
## GPA 0.22 0.07 3.00 3.0e-03 0.07 0.36 1.34 0.08
## TMS_total -0.41 0.07 -6.17 4.2e-09 -0.54 -0.28 1.10 0.19
##
## Residual Standard Error = 0.86 with 182 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.53 0.28 0.44 0.2 0.27 0.05 17.77 4 182 2.49e-12anova(lm_TMS_via_Uni_HAMNat_1_corr, lm_TMS_via_Uni_HAMNat_2a_corr, lm_TMS_via_Uni_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 184 176.7841 NA NA NA NA
## 2 183 161.7926 1 14.99147 20.39696 1.125325e-05
## 3 182 133.7674 1 28.02527 38.13036 4.207382e-09anova(lm_TMS_via_Uni_HAMNat_1_corr, lm_TMS_via_Uni_HAMNat_2b_corr, lm_TMS_via_Uni_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 184 176.7841 NA NA NA NA
## 2 183 140.3972 1 36.386956 49.507032 3.829059e-11
## 3 182 133.7674 1 6.629783 9.020289 3.045807e-03#Criterion: M1
#Correcting for range restriction
Cov_Mat_TMS_via_Uni_HAMNat_Incumbents_M1 <- cov((dplyr::select(data_TMS_via_Uni_HAMNat, Gender, Age, GPA, TMS_total, M1)), use = "complete.obs")
Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_TMS_via_Uni_HAMNat_Incumbents_M1, vnp = Cov_Mat_TMS_via_Uni_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1) <- colnames(Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'TMS_total', 'M1')
#Models
lm_TMS_via_Uni_HAMNat_M1_1_corr <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_1), plot = F)
lm_TMS_via_Uni_HAMNat_M1_2a_corr <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2a), plot = F)
lm_TMS_via_Uni_HAMNat_M1_2b_corr <- lmCor(M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2b), plot = F)
lm_TMS_via_Uni_HAMNat_M1_3_corr <- lmCor(M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_3), plot = F)
#Results
lm_TMS_via_Uni_HAMNat_M1_1_corr## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.17 0.11 -1.62 0.11 -0.38 0.04 1 0.03
## Age 0.11 0.11 1.02 0.31 -0.10 0.32 1 0.01
##
## Residual Standard Error = 0.99 with 87 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.2 0.04 0.19 0.04 0.02 0.04 1.74 2 87 0.181lm_TMS_via_Uni_HAMNat_M1_2a_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.18 0.09 -1.89 6.2e-02 -0.36 0.01 1.00 0.03
## Age -0.14 0.10 -1.33 1.9e-01 -0.35 0.07 1.27 -0.01
## GPA 0.54 0.10 5.14 1.7e-06 0.33 0.74 1.27 0.25
##
## Residual Standard Error = 0.87 with 86 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.51 0.26 0.38 0.14 0.24 0.07 10.31 3 86 7.25e-06lm_TMS_via_Uni_HAMNat_M1_2b_corr## Call: lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.13 0.1 -1.34 1.8e-01 -0.32 0.06 1.01 0.02
## Age 0.03 0.1 0.32 7.5e-01 -0.16 0.22 1.04 0.00
## TMS_total -0.43 0.1 -4.46 2.5e-05 -0.63 -0.24 1.04 0.19
##
## Residual Standard Error = 0.9 with 86 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.47 0.22 0.39 0.15 0.19 0.07 8.04 3 86 8.77e-05lm_TMS_via_Uni_HAMNat_M1_3_corr## Call: lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.14 0.09 -1.64 1.1e-01 -0.31 0.03 1.01 0.02
## Age -0.16 0.10 -1.65 1.0e-01 -0.35 0.03 1.28 -0.02
## GPA 0.45 0.10 4.52 1.9e-05 0.25 0.65 1.34 0.21
## TMS_total -0.34 0.09 -3.79 2.8e-04 -0.52 -0.16 1.10 0.15
##
## Residual Standard Error = 0.81 with 85 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.61 0.37 0.49 0.24 0.34 0.08 12.51 4 85 4.76e-08anova(lm_TMS_via_Uni_HAMNat_M1_1_corr, lm_TMS_via_Uni_HAMNat_M1_2a_corr, lm_TMS_via_Uni_HAMNat_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 87 85.56791 NA NA NA NA
## 2 86 65.46021 1 20.107694 30.51332 3.472916e-07
## 3 85 56.01337 1 9.446838 14.33553 2.843547e-04anova(lm_TMS_via_Uni_HAMNat_M1_1_corr, lm_TMS_via_Uni_HAMNat_M1_2b_corr, lm_TMS_via_Uni_HAMNat_M1_3_corr)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + TMS_total, data = Cor_Mat_TMS_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_TMS_via_Uni_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 87 85.56791 NA NA NA NA
## 2 86 69.50589 1 16.06201 24.37402 3.851124e-06
## 3 85 56.01337 1 13.49252 20.47483 1.948338e-05#Criterion: PCGPA
#Correcting for range restriction
Cov_Mat_HAMNat_via_Uni_HAMNat_Incumbents <- cov((dplyr::select(data_HAMNat_via_Uni_HAMNat, Gender, Age, GPA, HAMNat_total, PCGPA)), use = "complete.obs")
Cov_Mat_HAMNat_via_Uni_HAMNat_Testtakers <- cov((dplyr::select(data_HAMNat_Testtakers, Gender, Age, GPA, HAMNat_total)))
Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr <- lMvrrc(rcov = Cov_Mat_HAMNat_via_Uni_HAMNat_Incumbents, vnp = Cov_Mat_HAMNat_via_Uni_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr) <- colnames(Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'PCGPA')
#Models
lm_HAMNat_via_Uni_HAMNat_1_corr <- lmCor(PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_1), plot = F)
lm_HAMNat_via_Uni_HAMNat_2a_corr <- lmCor(PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2a), plot = F)
lm_HAMNat_via_Uni_HAMNat_2b_corr <- lmCor(PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2b), plot = F)
lm_HAMNat_via_Uni_HAMNat_3_corr <- lmCor(PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_3), plot = F)
#Results
lm_HAMNat_via_Uni_HAMNat_1_corr## Call: lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.06 -0.45 0.650 -0.14 0.09 1 0.00
## Age 0.14 0.06 2.41 0.016 0.03 0.25 1 0.02
##
## Residual Standard Error = 0.99 with 303 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.14 0.02 0.11 0.01 0.01 0.02 2.99 2 303 0.0516lm_HAMNat_via_Uni_HAMNat_2a_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.03 0.05 -0.58 5.6e-01 -0.14 0.07 1.0 0.00
## Age 0.00 0.06 -0.01 9.9e-01 -0.12 0.12 1.2 0.00
## GPA 0.34 0.06 5.70 2.8e-08 0.22 0.46 1.2 0.11
##
## Residual Standard Error = 0.95 with 302 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.34 0.11 0.26 0.07 0.11 0.03 13.05 3 302 4.88e-08lm_HAMNat_via_Uni_HAMNat_2b_corr## Call: lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.07 0.05 1.30 1.9e-01 -0.03 0.17 1.04 0.00
## Age 0.11 0.05 2.21 2.8e-02 0.01 0.21 1.00 0.02
## HAMNat_total -0.46 0.05 -8.92 4.5e-17 -0.56 -0.36 1.04 0.21
##
## Residual Standard Error = 0.89 with 302 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.47 0.22 0.33 0.11 0.22 0.04 29.05 3 302 1.57e-16lm_HAMNat_via_Uni_HAMNat_3_corr## Call: lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = PCGPA
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.05 0.05 1.02 3.1e-01 -0.05 0.15 1.05 0.00
## Age 0.03 0.05 0.55 5.8e-01 -0.08 0.14 1.21 0.00
## GPA 0.21 0.06 3.67 2.9e-04 0.10 0.32 1.32 0.07
## HAMNat_total -0.40 0.05 -7.60 3.9e-13 -0.51 -0.30 1.15 0.18
##
## Residual Standard Error = 0.87 with 301 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## PCGPA 0.51 0.26 0.4 0.16 0.25 0.04 26.05 4 301 1.47e-18anova(lm_HAMNat_via_Uni_HAMNat_1_corr, lm_HAMNat_via_Uni_HAMNat_2a_corr, lm_HAMNat_via_Uni_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2a), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 303 299.0896 NA NA NA NA
## 2 302 269.9936 1 29.09599 38.65561 1.678817e-09
## 3 301 226.5620 1 43.43161 57.70128 3.880077e-13anova(lm_HAMNat_via_Uni_HAMNat_1_corr, lm_HAMNat_via_Uni_HAMNat_2b_corr, lm_HAMNat_via_Uni_HAMNat_3_corr)## Model 1 = lmCor(y = PCGPA ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_1), plot = F)
## Model 2 = lmCor(y = PCGPA ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_2b), plot = F)
## Model 3 = lmCor(y = PCGPA ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_3), plot = F)## $PCGPA
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 303 299.0896 NA NA NA NA
## 2 302 236.6911 1 62.39847 82.89979 1.211895e-17
## 3 301 226.5620 1 10.12913 13.45710 2.885667e-04#Criterion: M1
#Correcting for range restriction
Cov_Mat_HAMNat_via_Uni_HAMNat_Incumbents_M1 <- cov((dplyr::select(data_HAMNat_via_Uni_HAMNat, Gender, Age, GPA, HAMNat_total, M1)), use = "complete.obs")
Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1 <- lMvrrc(rcov = Cov_Mat_HAMNat_via_Uni_HAMNat_Incumbents_M1, vnp = Cov_Mat_HAMNat_via_Uni_HAMNat_Testtakers, as_cor = T)
rownames(Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1) <- colnames(Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1) <- c('Gender', 'Age', 'GPA', 'HAMNat_total', 'M1')
#Models
lm_HAMNat_via_Uni_HAMNat_1_corr_M1 <- lmCor(M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_1), plot = F)
lm_HAMNat_via_Uni_HAMNat_2a_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2a), plot = F)
lm_HAMNat_via_Uni_HAMNat_2b_corr_M1 <- lmCor(M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2b), plot = F)
lm_HAMNat_via_Uni_HAMNat_3_corr_M1 <- lmCor(M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1, n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_3), plot = F)
#Results
lm_HAMNat_via_Uni_HAMNat_1_corr_M1## Call: lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_1), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.05 0.09 -0.56 0.5800 -0.22 0.12 1 0.00
## Age 0.28 0.09 3.23 0.0016 0.11 0.46 1 0.08
##
## Residual Standard Error = 0.97 with 120 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.29 0.08 0.23 0.05 0.07 0.05 5.34 2 120 0.006lm_HAMNat_via_Uni_HAMNat_2a_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2a), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender -0.06 0.08 -0.69 4.9e-01 -0.22 0.11 1.0 0.00
## Age 0.12 0.09 1.37 1.7e-01 -0.05 0.30 1.2 0.03
## GPA 0.39 0.09 4.41 2.3e-05 0.22 0.57 1.2 0.17
##
## Residual Standard Error = 0.9 with 119 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.46 0.21 0.4 0.16 0.19 0.06 10.6 3 119 3.15e-06lm_HAMNat_via_Uni_HAMNat_2b_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2b), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.02 0.08 0.27 7.9e-01 -0.14 0.19 1.04 0.00
## Age 0.26 0.08 3.21 1.7e-03 0.10 0.43 1.00 0.07
## HAMNat_total -0.35 0.08 -4.23 4.7e-05 -0.52 -0.19 1.04 0.13
##
## Residual Standard Error = 0.9 with 119 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.45 0.2 0.37 0.14 0.18 0.06 10.02 3 119 6.15e-06lm_HAMNat_via_Uni_HAMNat_3_corr_M1## Call: lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_3), plot = F)
##
## Multiple Regression from matrix input
##
## DV = M1
## slope se t p lower.ci upper.ci VIF Vy.x
## Gender 0.00 0.08 0.00 1.00000 -0.16 0.16 1.05 0.00
## Age 0.14 0.09 1.66 0.10000 -0.03 0.31 1.21 0.04
## GPA 0.31 0.09 3.42 0.00086 0.13 0.49 1.32 0.14
## HAMNat_total -0.27 0.08 -3.19 0.00180 -0.43 -0.10 1.15 0.10
##
## Residual Standard Error = 0.87 with 118 degrees of freedom
##
## Multiple Regression
## R R2 Ruw R2uw Shrunken R2 SE of R2 overall F df1 df2 p
## M1 0.52 0.27 0.47 0.22 0.25 0.06 11.11 4 118 1.11e-07anova(lm_HAMNat_via_Uni_HAMNat_1_corr_M1, lm_HAMNat_via_Uni_HAMNat_2a_corr_M1, lm_HAMNat_via_Uni_HAMNat_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + GPA, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2a), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 120 112.02953 NA NA NA NA
## 2 119 96.27904 1 15.750496 20.97154 1.155345e-05
## 3 118 88.62290 1 7.656133 10.19402 1.806488e-03anova(lm_HAMNat_via_Uni_HAMNat_1_corr_M1, lm_HAMNat_via_Uni_HAMNat_2b_corr_M1, lm_HAMNat_via_Uni_HAMNat_3_corr_M1)## Model 1 = lmCor(y = M1 ~ Gender + Age, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_1), plot = F)
## Model 2 = lmCor(y = M1 ~ Gender + Age + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_2b), plot = F)
## Model 3 = lmCor(y = M1 ~ Gender + Age + GPA + HAMNat_total, data = Cor_Mat_HAMNat_via_Uni_HAMNat_Incumbents_Corr_M1,
## n.obs = nobs(lm_HAMNat_via_Uni_HAMNat_M1_3), plot = F)## $M1
## Res Df Res SS Diff df Diff SS F Pr(F > )
## 1 120 112.02953 NA NA NA NA
## 2 119 97.40004 1 14.629490 19.47893 2.249934e-05
## 3 118 88.62290 1 8.777139 11.68662 8.647961e-04#Criterion: PCGPA
#Correcting for range restriction
Cov_Mat_TMS_Testtakers_Subtests <- cov((dplyr::select(data_TMS_Testtakers, Gender, Age, GPA, BMS, QFP, DT, TC, MRT, FMT, VMT, VST)))
Cov_Mat_TMS_Incumbents_Subtests <- cov((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, BMS, QFP, DT, TC, MRT, FMT, VMT, VST, PCGPA)), use = "complete.obs")
Cor_Mat_TMS_Incumbents_Subtests <- cor((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, BMS, QFP, DT, TC, MRT, FMT, VMT, VST, PCGPA)), use = "complete.obs")
Cor_Mat_Corr_TMS_Incumbents_Subtests <- lMvrrc(rcov = Cov_Mat_TMS_Incumbents_Subtests, vnp = Cov_Mat_TMS_Testtakers_Subtests, as_cor = T)
rownames(Cor_Mat_Corr_TMS_Incumbents_Subtests) <- colnames(Cor_Mat_Corr_TMS_Incumbents_Subtests) <- c('Gender', 'Age', 'GPA', 'BMS', 'QFP', 'DT', 'TC', 'MRT', 'FMT', 'VMT', 'VST', 'PCGPA')
#Results
round(Cor_Mat_TMS_Incumbents_Subtests, 2)## Gender Age GPA BMS QFP DT TC MRT FMT VMT VST PCGPA
## Gender 1.00 0.06 0.10 0.11 0.21 0.16 0.14 0.08 -0.14 -0.12 -0.02 -0.09
## Age 0.06 1.00 0.59 -0.12 -0.19 -0.18 -0.08 -0.06 -0.07 -0.05 -0.07 0.12
## GPA 0.10 0.59 1.00 -0.09 -0.18 -0.17 -0.06 0.02 -0.04 0.00 -0.01 0.14
## BMS 0.11 -0.12 -0.09 1.00 0.47 0.52 0.59 0.26 0.21 0.25 0.16 -0.17
## QFP 0.21 -0.19 -0.18 0.47 1.00 0.57 0.41 0.27 0.17 0.18 0.20 -0.21
## DT 0.16 -0.18 -0.17 0.52 0.57 1.00 0.46 0.27 0.16 0.19 0.21 -0.14
## TC 0.14 -0.08 -0.06 0.59 0.41 0.46 1.00 0.25 0.20 0.23 0.14 -0.12
## MRT 0.08 -0.06 0.02 0.26 0.27 0.27 0.25 1.00 0.37 0.37 0.38 -0.09
## FMT -0.14 -0.07 -0.04 0.21 0.17 0.16 0.20 0.37 1.00 0.40 0.31 -0.01
## VMT -0.12 -0.05 0.00 0.25 0.18 0.19 0.23 0.37 0.40 1.00 0.31 -0.07
## VST -0.02 -0.07 -0.01 0.16 0.20 0.21 0.14 0.38 0.31 0.31 1.00 -0.09
## PCGPA -0.09 0.12 0.14 -0.17 -0.21 -0.14 -0.12 -0.09 -0.01 -0.07 -0.09 1.00round(Cor_Mat_Corr_TMS_Incumbents_Subtests, 2)## Gender Age GPA BMS QFP DT TC MRT FMT VMT VST PCGPA
## Gender 1.00 0.05 0.03 0.12 0.23 0.18 0.12 0.08 -0.08 -0.09 -0.01 -0.10
## Age 0.05 1.00 0.46 -0.12 -0.18 -0.17 -0.09 -0.09 -0.10 -0.08 -0.09 0.11
## GPA 0.03 0.46 1.00 -0.25 -0.30 -0.28 -0.21 -0.12 -0.13 -0.14 -0.09 0.19
## BMS 0.12 -0.12 -0.25 1.00 0.54 0.59 0.64 0.36 0.27 0.33 0.26 -0.21
## QFP 0.23 -0.18 -0.30 0.54 1.00 0.62 0.49 0.36 0.24 0.28 0.26 -0.25
## DT 0.18 -0.17 -0.28 0.59 0.62 1.00 0.55 0.35 0.26 0.28 0.26 -0.18
## TC 0.12 -0.09 -0.21 0.64 0.49 0.55 1.00 0.36 0.28 0.33 0.25 -0.17
## MRT 0.08 -0.09 -0.12 0.36 0.36 0.35 0.36 1.00 0.43 0.43 0.44 -0.13
## FMT -0.08 -0.10 -0.13 0.27 0.24 0.26 0.28 0.43 1.00 0.46 0.35 -0.05
## VMT -0.09 -0.08 -0.14 0.33 0.28 0.28 0.33 0.43 0.46 1.00 0.35 -0.11
## VST -0.01 -0.09 -0.09 0.26 0.26 0.26 0.25 0.44 0.35 0.35 1.00 -0.12
## PCGPA -0.10 0.11 0.19 -0.21 -0.25 -0.18 -0.17 -0.13 -0.05 -0.11 -0.12 1.00#Criterion: M1
#Correcting for range restriction
Cov_Mat_TMS_Incumbents_M1_Subtests <- cov((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, BMS, QFP, DT, TC, MRT, FMT, VMT, VST, M1)), use = "complete.obs")
Cor_Mat_TMS_Incumbents_M1_Subtests <- cor((dplyr::select(data_TMS_Incumbents, Gender, Age, GPA, BMS, QFP, DT, TC, MRT, FMT, VMT, VST, M1)), use = "complete.obs")
Cor_Mat_Corr_TMS_Incumbents_M1_Subtests <- lMvrrc(rcov = Cov_Mat_TMS_Incumbents_M1_Subtests, vnp = Cov_Mat_TMS_Testtakers_Subtests, as_cor = T)
rownames(Cor_Mat_Corr_TMS_Incumbents_M1_Subtests) <- colnames(Cor_Mat_Corr_TMS_Incumbents_M1_Subtests) <- c('Gender', 'Age', 'GPA', 'BMS', 'QFP', 'DT', 'TC', 'MRT', 'FMT', 'VMT', 'VST', 'M1')
#Results
round(Cor_Mat_TMS_Incumbents_M1_Subtests, 2)## Gender Age GPA BMS QFP DT TC MRT FMT VMT VST M1
## Gender 1.00 0.04 0.11 0.04 0.22 0.11 0.07 -0.04 -0.23 -0.24 0.00 -0.12
## Age 0.04 1.00 0.64 -0.20 -0.19 -0.13 -0.14 -0.03 0.00 0.09 0.00 0.18
## GPA 0.11 0.64 1.00 -0.19 -0.15 -0.15 -0.10 -0.04 -0.08 0.02 -0.01 0.21
## BMS 0.04 -0.20 -0.19 1.00 0.47 0.56 0.59 0.24 0.15 0.25 0.23 -0.30
## QFP 0.22 -0.19 -0.15 0.47 1.00 0.57 0.36 0.28 0.12 0.19 0.20 -0.20
## DT 0.11 -0.13 -0.15 0.56 0.57 1.00 0.44 0.31 0.17 0.25 0.31 -0.24
## TC 0.07 -0.14 -0.10 0.59 0.36 0.44 1.00 0.14 0.13 0.20 0.19 -0.22
## MRT -0.04 -0.03 -0.04 0.24 0.28 0.31 0.14 1.00 0.36 0.34 0.32 -0.08
## FMT -0.23 0.00 -0.08 0.15 0.12 0.17 0.13 0.36 1.00 0.37 0.25 0.02
## VMT -0.24 0.09 0.02 0.25 0.19 0.25 0.20 0.34 0.37 1.00 0.25 0.03
## VST 0.00 0.00 -0.01 0.23 0.20 0.31 0.19 0.32 0.25 0.25 1.00 -0.02
## M1 -0.12 0.18 0.21 -0.30 -0.20 -0.24 -0.22 -0.08 0.02 0.03 -0.02 1.00round(Cor_Mat_Corr_TMS_Incumbents_M1_Subtests, 2)## Gender Age GPA BMS QFP DT TC MRT FMT VMT VST M1
## Gender 1.00 0.05 0.03 0.12 0.23 0.18 0.12 0.08 -0.08 -0.09 -0.01 -0.15
## Age 0.05 1.00 0.46 -0.12 -0.18 -0.17 -0.09 -0.09 -0.10 -0.08 -0.09 0.12
## GPA 0.03 0.46 1.00 -0.25 -0.30 -0.28 -0.21 -0.12 -0.13 -0.14 -0.09 0.26
## BMS 0.12 -0.12 -0.25 1.00 0.54 0.59 0.64 0.36 0.27 0.33 0.26 -0.35
## QFP 0.23 -0.18 -0.30 0.54 1.00 0.62 0.49 0.36 0.24 0.28 0.26 -0.27
## DT 0.18 -0.17 -0.28 0.59 0.62 1.00 0.55 0.35 0.26 0.28 0.26 -0.30
## TC 0.12 -0.09 -0.21 0.64 0.49 0.55 1.00 0.36 0.28 0.33 0.25 -0.29
## MRT 0.08 -0.09 -0.12 0.36 0.36 0.35 0.36 1.00 0.43 0.43 0.44 -0.15
## FMT -0.08 -0.10 -0.13 0.27 0.24 0.26 0.28 0.43 1.00 0.46 0.35 -0.05
## VMT -0.09 -0.08 -0.14 0.33 0.28 0.28 0.33 0.43 0.46 1.00 0.35 -0.04
## VST -0.01 -0.09 -0.09 0.26 0.26 0.26 0.25 0.44 0.35 0.35 1.00 -0.05
## M1 -0.15 0.12 0.26 -0.35 -0.27 -0.30 -0.29 -0.15 -0.05 -0.04 -0.05 1.00#Criterion: PCGPA
#Correcting for range restriction
Cov_Mat_HAMNat_Testtakers_Subtests <- cov((dplyr::select(data_HAMNat_Testtakers, Gender, Age, GPA, KT, NRT, VRT)))
Cov_Mat_HAMNat_Incumbents_Subtests <- cov((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, KT, NRT, VRT, PCGPA)), use = "complete.obs")
Cor_Mat_HAMNat_Incumbents_Subtests <- cor((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, KT, NRT, VRT, PCGPA)), use = "complete.obs")
Cor_Mat_Corr_HAMNat_Incumbents_Subtests <- lMvrrc(rcov = Cov_Mat_HAMNat_Incumbents_Subtests, vnp = Cov_Mat_HAMNat_Testtakers_Subtests, as_cor = T)
rownames(Cor_Mat_Corr_HAMNat_Incumbents_Subtests) <- colnames(Cor_Mat_Corr_HAMNat_Incumbents_Subtests) <- c('Gender', 'Age', 'GPA', 'KT', 'NRT', 'VRT', 'PCGPA')
#Results
round(Cor_Mat_HAMNat_Incumbents_Subtests, 2)## Gender Age GPA KT NRT VRT PCGPA
## Gender 1.00 0.04 0.09 0.19 0.23 -0.04 -0.03
## Age 0.04 1.00 0.55 -0.05 -0.07 -0.10 0.07
## GPA 0.09 0.55 1.00 -0.08 -0.07 -0.07 0.15
## KT 0.19 -0.05 -0.08 1.00 0.23 0.23 -0.34
## NRT 0.23 -0.07 -0.07 0.23 1.00 0.30 -0.15
## VRT -0.04 -0.10 -0.07 0.23 0.30 1.00 -0.09
## PCGPA -0.03 0.07 0.15 -0.34 -0.15 -0.09 1.00round(Cor_Mat_Corr_HAMNat_Incumbents_Subtests, 2)## Gender Age GPA KT NRT VRT PCGPA
## Gender 1.00 0.02 0.03 0.19 0.24 0.01 -0.03
## Age 0.02 1.00 0.41 -0.03 -0.10 -0.14 0.05
## GPA 0.03 0.41 1.00 -0.27 -0.18 -0.17 0.22
## KT 0.19 -0.03 -0.27 1.00 0.29 0.27 -0.35
## NRT 0.24 -0.10 -0.18 0.29 1.00 0.33 -0.17
## VRT 0.01 -0.14 -0.17 0.27 0.33 1.00 -0.11
## PCGPA -0.03 0.05 0.22 -0.35 -0.17 -0.11 1.00#Criterion: M1
#Correcting for range restriction
Cov_Mat_HAMNat_Incumbents_M1_Subtests <- cov((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, KT, NRT, VRT, M1)), use = "complete.obs")
Cor_Mat_HAMNat_Incumbents_M1_Subtests <- cor((dplyr::select(data_HAMNat_Incumbents, Gender, Age, GPA, KT, NRT, VRT, M1)), use = "complete.obs")
Cor_Mat_Corr_HAMNat_Incumbents_M1_Subtests <- lMvrrc(rcov = Cov_Mat_HAMNat_Incumbents_M1_Subtests, vnp = Cov_Mat_HAMNat_Testtakers_Subtests, as_cor = T)
rownames(Cor_Mat_Corr_HAMNat_Incumbents_M1_Subtests) <- colnames(Cor_Mat_Corr_HAMNat_Incumbents_M1_Subtests) <- c('Gender', 'Age', 'GPA', 'KT', 'NRT', 'VRT', 'M1')
#Results
round(Cor_Mat_HAMNat_Incumbents_M1_Subtests, 2)## Gender Age GPA KT NRT VRT M1
## Gender 1.00 0.09 0.11 0.21 0.15 -0.04 -0.10
## Age 0.09 1.00 0.58 -0.09 -0.06 -0.08 0.24
## GPA 0.11 0.58 1.00 -0.11 -0.05 -0.10 0.28
## KT 0.21 -0.09 -0.11 1.00 0.30 0.20 -0.46
## NRT 0.15 -0.06 -0.05 0.30 1.00 0.18 -0.23
## VRT -0.04 -0.08 -0.10 0.20 0.18 1.00 -0.09
## M1 -0.10 0.24 0.28 -0.46 -0.23 -0.09 1.00round(Cor_Mat_Corr_HAMNat_Incumbents_M1_Subtests, 2)## Gender Age GPA KT NRT VRT M1
## Gender 1.00 0.02 0.03 0.19 0.24 0.01 -0.11
## Age 0.02 1.00 0.41 -0.03 -0.10 -0.14 0.19
## GPA 0.03 0.41 1.00 -0.27 -0.18 -0.17 0.36
## KT 0.19 -0.03 -0.27 1.00 0.29 0.27 -0.47
## NRT 0.24 -0.10 -0.18 0.29 1.00 0.33 -0.25
## VRT 0.01 -0.14 -0.17 0.27 0.33 1.00 -0.15
## M1 -0.11 0.19 0.36 -0.47 -0.25 -0.15 1.00