## Italy WS-TD Inequity Game library(readr) WS_IA_data <- read.csv("Inequity_Game_Trial_by_Trial.csv") # install packages: lme4, reshape2, binom, multcomp, optimx, data.table, nlme library(nlme) library(lme4) library(reshape2) library(binom) library(multcomp) library(optimx) library(data.table) library(plyr) is.numeric(WS_IA_data$Trial_Num) WS_IA_data$ID <- as.factor(WS_IA_data$ID) WS_IA_data$Order <- as.factor(WS_IA_data$Order) WS_IA_data$Group <- as.factor(WS_IA_data$Group) WS_IA_data$Condition <- as.factor(WS_IA_data$Condition) WS_IA_data$Distribution <- as.factor(WS_IA_data$Distribution) WS_IA_data$Decision <- as.factor(WS_IA_data$Decision) is.factor(WS_IA_data$ID) ws.0 <- glmer (Decision ~ 1 + (1|ID), data = WS_IA_data, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.1 <- glmer (Decision ~ (Distribution + Condition + Group)^3 + (1|ID), data = WS_IA_data, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.0,ws.1) # better fit with ws.1 summary(ws.1) # distribution x condition interaction so subset by condition ## Figure to show 3-way interaction IG_count <- read.csv("IG_count.csv") IG_count$Group <- as.factor(IG_count$Group) IG_count$Condition <- as.factor(IG_count$Condition) IG_count$Distribution <- as.factor(IG_count$Distribution) levels(IG_count$Distribution) IG_count$Distribution <- relevel(IG_count$Distribution, ref = "E") # boxplox jmv::descriptives( formula = Rejections ~ Group:Condition:Distribution, data = IG_count, freq = TRUE, box = TRUE, dot = TRUE, dotType = "stack", boxLabelOutliers = FALSE) WS_Adv <- subset(WS_IA_data, Condition=="Adv") WS_Disadv <- subset(WS_IA_data, Condition=="Disadv") ## Disadvantageous models ws.disadv.0 <- glmer (Decision ~ 1 + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.disadv.1 <- glmer (Decision ~ Distribution * Group + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.disadv.0,ws.disadv.1) # some improvement in fit over null, p = .073 summary(ws.disadv.1) # only distribution sig, interaction ns # test main effects model ws.disadv.2 <- glmer (Decision ~ Distribution + Group + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.disadv.0,ws.disadv.2) # improvement over null, p = .0322 summary(ws.disadv.2) # no diff between groups; higher rejections of unequal than equal for all ## does adding other variables improve fit over model 2? ws.disadv.3 <- glmer (Decision ~ Distribution + Group + Trial_Num + Order + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.disadv.2,ws.disadv.3) # no improvement ## add MA, CA and IQ as covariates ws.disadv.4 <- glmer (Decision ~ Distribution + Group + MA + CA + IQ + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.disadv.2,ws.disadv.4) # no improvement # Based on Reviewer 2 and given results for Adv below with MA, test interactions ws.disadv.5a <- glmer (Decision ~ (Distribution + Group) * MA + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) summary(ws.disadv.5a) # get MA effect with Group, trend for interaction when use CA, no effect for IQ # no Distribution x Group effect ws.disadv.5 <- glmer (Decision ~ Distribution + Group * MA + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.disadv.2,ws.disadv.5) # improved fit over just main effects summary(ws.disadv.5) library(emmeans) emtrends(ws.disadv.5, ~Group, var="MA") # here see sig more rejections with MA for TD only (0.45, LCI = .11, UCI = .80) # note that this collapses Distribution # need 3-way interaction model to visualize ws.disadv.6 <- glmer (Decision ~ (Distribution + Group + MA)^3 + (1|ID), data = WS_Disadv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) summary(ws.disadv.6) library(ggplot2) library(interactions) library(jtools) library(effects) library(ggpubr) library(scales) interact_plot(ws.disadv.6, pred = "MA", modx = "Distribution", mod2 = "Group", interval=TRUE, vary.lty = FALSE, colors="Qual1", x.label="Mental Age (yrs)", y.label="Probability of Rejecting", modx.labels = c("Equal","Unequal"), mod2.labels = c("TD","WS"), main.title = c("Disadvantageous Condition: Group x Mental Age")) + theme_apa(legend.pos="top") + scale_x_continuous(breaks=seq(4,9,1), limits=c(4,9)) + scale_y_continuous(breaks=seq(0,1,.25), limits=c(0,1)) + theme(plot.title = element_text(hjust = 0.5)) + theme(panel.background = element_rect(fill = 'white', colour = 'black')) ggsave("IG_Disadv_Group_MA.tiff", dpi=300, height=4, width=5, units="in") ## Advantageous models ws.adv.0 <- glmer (Decision ~ 1 + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.adv.1 <- glmer (Decision ~ Distribution * Group + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.0,ws.adv.1) # improved fit over null, p = .0018 summary(ws.adv.1) # only distribution sig at p = .054; interaction not sig # test main effects model ws.adv.2 <- glmer (Decision ~ Distribution + Group + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.0,ws.adv.2) anova(ws.adv.1,ws.adv.2) # improved fit over null, p < .0013; not improved over interaction model so go with simpler model (ws.adv.2) summary(ws.adv.2) # only distribution significant, higher rejections of equal ## does adding other variables improve fit over model 2? ws.adv.3 <- glmer (Decision ~ Distribution + Group + Trial_Num + Order + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.3) # no improvement # add MA and IQ as covariates ws.adv.4 <- glmer (Decision ~ Distribution + Group + MA + IQ + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.4) # no improvement # final model just main effects of distribution and group ## Given the higher rejections of equal trials, test if this effect increases over trials ws.adv.5 <- glmer (Decision ~ (Distribution + Group + Trial_Num)^3 + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.adv.5 <- glmer (Decision ~ (Distribution + Group) * Trial_Num + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.adv.5 <- glmer (Decision ~ Group + Distribution * Trial_Num + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) ws.adv.5 <- glmer (Decision ~ Group + Distribution + Trial_Num + (1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.5) summary(ws.adv.5) ## none improve fit over main effects model ## Reviewer questions about effects of MA and CA on rejections (also IQ) ws.adv.5 <- glmer (Decision ~ Distribution + Group * MA +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.5) summary(ws.adv.5) # adding MA interaction with Group improves fit, p = .04; no effect for CA or IQ # test interaction with Distribution ws.adv.6 <- glmer (Decision ~ (Distribution + Group) * MA +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.6) # no improvement summary(ws.adv.6) # same interaction wiht MA, none with Distribution ws.adv.6 <- glmer (Decision ~ (Distribution + Group + MA)^3 +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.6) # no improvement # try CA ws.adv.6 <- glmer (Decision ~ (Distribution + Group) * CA +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) anova(ws.adv.2,ws.adv.6) # no improvement # final model for Adv ws.adv.5 <- glmer (Decision ~ Distribution + Group * MA +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) #ws.adv.5 <- glmer (Decision ~ Distribution + Group * MA + CA +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) summary(ws.adv.5) # interaction p = .02; same when add CA to model as control # do not get same when use IQ instead of MA library(performance) check_outliers(ws.adv.5, method=c("mahalanobis")) # no outliers detected library(emmeans) emtrends(ws.adv.5, ~Group, var="MA") # simple slopes show no diff for TD by MA (0.23, SE=.25; LCI = -.255, UCI = .73) # but sig neg slope for WS (-.054, SE = .23, LCI=-.98, UCI = -.09) ## Conclusion - fewer rejections overall with increasing MA for WS ## this suggests that increased cognitive abilities, as opposed to life experience lead to more typical pattern for AI ## this holds when add CA to model as control variable # to show both groups and distribution, used 3-way interaction model ws.adv.6 <- glmer (Decision ~ (Distribution + Group + MA)^3 +(1|ID), data = WS_Adv, family = binomial, control = glmerControl(optimizer = "optimx", calc.derivs = FALSE,optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE))) interact_plot(ws.adv.6, pred = "MA", modx = "Distribution", mod2 = "Group", interval=TRUE, vary.lty = FALSE, colors="Qual1", x.label="Mental Age (yrs)", y.label="Probability of Rejecting", modx.labels = c("Equal","Unequal"), mod2.labels = c("TD","WS"), main.title = c("Advantageous Condition: Group x Mental Age")) + theme_apa(legend.pos="top") + scale_x_continuous(breaks=seq(4,9,1), limits=c(4,9)) + scale_y_continuous(breaks=seq(0,1,.25), limits=c(0,1)) + theme(plot.title = element_text(hjust = 0.5)) + theme(panel.background = element_rect(fill = 'white', colour = 'black')) ggsave("IG_Adv_Group_MA.tiff", dpi=300, height=4, width=5, units="in")