Rainfall as driver of Australian AIV outbreaks
Marcel Klaassen
30 July 2021
knitr::opts_chunk$set(echo = TRUE)
library(jtools)
library (performance) #for pseudo R2
library(ggplot2)
library(tidyr) #for long format
library(zoo) #for running mean
try(setwd("E:/OneDrive - Deakin University/Active projects/Marti"))
#read MDB rainfall data downloaded from BOM
R <- read.csv("latest.22233.csv")
#select all years past 1965
R <- R[which(R$Year>1965),]
#make long format
S <- gather(R,key="Month",value="rainfall",-Year) #uses tidyr
S$month <- match(S$Month,month.abb) #recode month to numbers
S <- S[order(c(S$Year,S$month)),]
S <- S[which(!is.na(S$rainfall)),] #remove missing cases
#The outbreak dataframe
O <- data.frame(Year =c(1976, 1985, 1992, 1992, 1994, 1997, 2006, 2010, 2012, 2012, 2012, 2012, 2013, 2020, 2020, 2020),
month=c( 1, 5, 7, 8, 12, 11, 10, 3, 1, 4, 5, 11, 10, 7, 8, 9),
HL=c( "H", "H", "L", "H", "H", "H", "L", "L", "L", "L", "L", "H", "H", "H", "L", "L"))
O$outbreak <- 1
I <- merge(S,O, by=c("Year","month"), all.x=TRUE)
I$outbreak[which(is.na(I$outbreak))] <- 0
I <- I[!duplicated(I),] #remove months where there are multiple outbreaks in 1 monthOutbreaks in poultry in relation to rainfall
The underlying rainfall data are the monthly rainfall data across the entire Murray Darling Basin up till and including October 2020, which were downloaded from http://www.bom.gov.au/climate/change/index.shtml#tabs=Tracker&tracker=timeseries&tQ=graph%3Drain%26area%3Dmdb%26season%3Dallmonths%26ave_yr%3D0
Rainfall period
The number of months across which rainfall is being averaged
Time-lag period
The number of months following the rainfall period until the outbreak. It is assumed that after a major rainfall period
it takes a while for naive ducks to enter the population,
for the environment to dry out
for birds to start aggregating
for an epizootic to evolve
once spill over of LPAI from wild birds into poultry has taken place for a HPAI to evolve
Statistics
We used generalised linear modelling to conduct a logistic regression across all months from January 1970 until October 2020, where we scored an outbreak month as 1 and a non-outbreak month as 0 as dependent variable.
To appropriately weight co-occurring outbreaks (i.e. outbreaks happening within the same months of the same year), one of the outbreaks was moved to the following month.
We ran 600 models where in each model we used rainfall as the explanatory variable calculated for a different combination of rainfall period and time-lag period.
Below the output of the best model is printed
#define the output df
M <- data.frame(AIC = numeric(700))
M$r2 <- NA
M$coef <- NA
M$RainfallPeriod <- NA
M$TimeLagPeriod <- NA
M$N <- NA
i <- 0
for (r in 1:24) { #number of rainfall months
for (t in 0:(24)) { #time-lag months
i <- i+1
I$rainmean <- NA
for (j in (r+t+1):nrow(I)) {
I$rainmean[j] <- mean(c(I$rainfall[(j-t-r):(j-t-1)]))
}
model <- glm(outbreak ~ rainmean, data=I[which(I$Year %in% c(1970:2020)),],family=binomial)
#summ(model)
M$AIC[i] <- model$aic
M$r2[i] <- r2(model)$R2_Tjur
M$coef[i] <- model$coefficients[2]
M$N[i] <- length(model$residuals)
#get the rainfall and time-lag periods
M$RainfallPeriod[i] <- r
M$TimeLagPeriod[i] <- t
}
}
#arrange df starting with lowest AIC
M <- M[order(M$AIC),]
M <- M[which(!is.na(M$r2)),]
#make a marker for top models
M$top <- ifelse(M$AIC <= min(M$AIC)+2,"X","")
#how many top models do we have?
TOP <- length(M$top[which(M$top=="X")])
#make variable to store TOP model predictions
#add fitted values from best model as Expected Probabilities
I$fit <- NA
I$fit[48:658] <- 0
#run best models
for (i in 1:TOP) {
I$rainmean <- NA
r <- M$RainfallPeriod[i]
t <- M$TimeLagPeriod[i]
for (j in (r+t+1):nrow(I)) {
I$rainmean[j] <- mean(c(I$rainfall[(j-t-r):(j-t-1)]))
}
model <- glm(outbreak ~ rainmean, data=I[which(I$Year %in% c(1970:2020)),],family=binomial)
print(summary(model))
I$fit[48:658] <- model$fitted.values + I$fit[48:658]
}##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6469 -0.2493 -0.1950 -0.1589 3.2142
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -7.0098 1.2070 -5.807 6.34e-09 ***
## rainmean 0.0778 0.0251 3.100 0.00194 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.11 on 608 degrees of freedom
## AIC: 143.11
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5779 -0.2480 -0.1943 -0.1591 3.2014
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.92039 1.17870 -5.871 4.33e-09 ***
## rainmean 0.07563 0.02440 3.100 0.00194 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.13 on 608 degrees of freedom
## AIC: 143.13
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5921 -0.2495 -0.1967 -0.1607 3.2115
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -7.07452 1.23151 -5.745 9.22e-09 ***
## rainmean 0.07944 0.02573 3.088 0.00202 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.16 on 608 degrees of freedom
## AIC: 143.16
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5800 -0.2495 -0.1956 -0.1593 3.1926
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.98777 1.20566 -5.796 6.8e-09 ***
## rainmean 0.07734 0.02509 3.083 0.00205 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.20 on 608 degrees of freedom
## AIC: 143.2
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6247 -0.2481 -0.1947 -0.1603 3.1939
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.87061 1.17788 -5.833 5.44e-09 ***
## rainmean 0.07456 0.02443 3.051 0.00228 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.42 on 608 degrees of freedom
## AIC: 143.42
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5687 -0.2491 -0.1943 -0.1600 3.1767
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.78108 1.15148 -5.889 3.89e-09 ***
## rainmean 0.07236 0.02377 3.045 0.00233 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.44 on 608 degrees of freedom
## AIC: 143.44
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6484 -0.2452 -0.1959 -0.1620 3.1915
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.22104 0.96312 -6.459 1.05e-10 ***
## rainmean 0.05858 0.01905 3.076 0.0021 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.44 on 608 degrees of freedom
## AIC: 143.44
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6477 -0.2455 -0.1958 -0.1632 3.1666
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.01829 0.90283 -6.666 2.63e-11 ***
## rainmean 0.05373 0.01757 3.059 0.00222 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.59 on 608 degrees of freedom
## AIC: 143.59
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5655 -0.2478 -0.1972 -0.1628 3.2089
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -7.00255 1.24993 -5.602 2.11e-08 ***
## rainmean 0.07814 0.02635 2.965 0.00302 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.87 on 608 degrees of freedom
## AIC: 143.87
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5944 -0.2500 -0.1994 -0.1640 3.1873
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.91329 1.22598 -5.639 1.71e-08 ***
## rainmean 0.07600 0.02577 2.949 0.00318 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 139.95 on 608 degrees of freedom
## AIC: 143.95
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5543 -0.2492 -0.1968 -0.1627 3.1377
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.66302 1.14693 -5.809 6.27e-09 ***
## rainmean 0.06987 0.02379 2.937 0.00332 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.05 on 608 degrees of freedom
## AIC: 144.05
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5434 -0.2487 -0.1978 -0.1630 3.1323
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.73353 1.17225 -5.744 9.24e-09 ***
## rainmean 0.07166 0.02445 2.930 0.00339 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.09 on 608 degrees of freedom
## AIC: 144.09
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6279 -0.2425 -0.1982 -0.1665 3.1724
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.77816 0.84554 -6.834 8.28e-12 ***
## rainmean 0.04816 0.01621 2.970 0.00297 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.11 on 608 degrees of freedom
## AIC: 144.11
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6320 -0.2456 -0.1969 -0.1654 3.1868
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.94413 0.90070 -6.599 4.13e-11 ***
## rainmean 0.05222 0.01762 2.964 0.00304 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.12 on 608 degrees of freedom
## AIC: 144.12
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5643 -0.2522 -0.1997 -0.1640 3.1062
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.48606 1.11026 -5.842 5.16e-09 ***
## rainmean 0.06576 0.02296 2.864 0.00418 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.46 on 608 degrees of freedom
## AIC: 144.46
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5717 -0.2447 -0.2001 -0.1668 3.1324
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.20916 1.01578 -6.113 9.8e-10 ***
## rainmean 0.05894 0.02059 2.862 0.0042 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.54 on 608 degrees of freedom
## AIC: 144.54
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6047 -0.2430 -0.1980 -0.1699 3.1087
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.53649 0.78888 -7.018 2.25e-12 ***
## rainmean 0.04260 0.01489 2.861 0.00422 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.72 on 608 degrees of freedom
## AIC: 144.72
##
## Number of Fisher Scoring iterations: 6
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5790 -0.2405 -0.1978 -0.1710 3.0989
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.38507 0.73944 -7.283 3.27e-13 ***
## rainmean 0.03890 0.01361 2.858 0.00426 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.75 on 608 degrees of freedom
## AIC: 144.75
##
## Number of Fisher Scoring iterations: 6
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6077 -0.2438 -0.2006 -0.1692 3.0828
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.68619 0.84223 -6.751 1.46e-11 ***
## rainmean 0.04631 0.01627 2.846 0.00443 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.77 on 608 degrees of freedom
## AIC: 144.77
##
## Number of Fisher Scoring iterations: 6
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5888 -0.2463 -0.2000 -0.1676 3.1046
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.01061 0.95652 -6.284 3.3e-10 ***
## rainmean 0.05424 0.01917 2.830 0.00466 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.77 on 608 degrees of freedom
## AIC: 144.77
##
## Number of Fisher Scoring iterations: 6
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5572 -0.2498 -0.2008 -0.1665 3.1431
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.66251 1.19544 -5.573 2.5e-08 ***
## rainmean 0.07038 0.02520 2.793 0.00523 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.81 on 608 degrees of freedom
## AIC: 144.81
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.6049 -0.2431 -0.2006 -0.1697 3.1500
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.67401 0.84225 -6.737 1.62e-11 ***
## rainmean 0.04606 0.01629 2.827 0.0047 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 140.87 on 608 degrees of freedom
## AIC: 144.87
##
## Number of Fisher Scoring iterations: 6
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5241 -0.2483 -0.2008 -0.1680 3.1719
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.75721 1.24454 -5.429 5.65e-08 ***
## rainmean 0.07282 0.02648 2.750 0.00596 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 141.04 on 608 degrees of freedom
## AIC: 145.04
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5462 -0.2498 -0.2001 -0.1673 3.0814
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.46194 1.14030 -5.667 1.45e-08 ***
## rainmean 0.06559 0.02387 2.748 0.006 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 141.05 on 608 degrees of freedom
## AIC: 145.05
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5624 -0.2504 -0.2024 -0.1691 3.1538
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.68347 1.22163 -5.471 4.48e-08 ***
## rainmean 0.07101 0.02591 2.741 0.00613 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 141.09 on 608 degrees of freedom
## AIC: 145.09
##
## Number of Fisher Scoring iterations: 7
##
##
## Call:
## glm(formula = outbreak ~ rainmean, family = binomial, data = I[which(I$Year %in%
## c(1970:2020)), ])
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.5468 -0.2524 -0.2016 -0.1672 3.0747
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.35701 1.10565 -5.750 8.95e-09 ***
## rainmean 0.06303 0.02301 2.739 0.00615 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 148.08 on 609 degrees of freedom
## Residual deviance: 141.11 on 608 degrees of freedom
## AIC: 145.11
##
## Number of Fisher Scoring iterations: 7I$fit <- I$fit/TOP #to get the average fitted values across the top modelsOverview plot of model results
For each model the AIC was calculated and we classified as the top models the models that where within 2 AIC units of the model with the minimal AIC.
Below a plot of the AIC values is presented with combinations marked with a white X identifying the top models.
P <- ggplot(data=M, aes(x=RainfallPeriod,y=TimeLagPeriod, fill=AIC))+
geom_tile() +
theme_classic() +
geom_text(aes(x=RainfallPeriod, y=TimeLagPeriod, label = top), color = "white", size = 3) +
theme(aspect.ratio=1, legend.position="top", legend.text=element_text(angle=90,vjust = 0.5, hjust=0.5),
legend.direction = "horizontal") +
labs(y = "Time-lag period (months)",
x = "Rainfall period (months)")
plot(P)
png("plot MDB rain and outbreaks AIC.png", width = 120, height = 90, units='mm', res = 600)
print(P)
dev.off()## png
## 2Same plot with coefficient
P <- ggplot(data=M, aes(x=RainfallPeriod,y=TimeLagPeriod, fill=coef))+
geom_tile() +
theme_classic() +
geom_text(aes(x=RainfallPeriod, y=TimeLagPeriod, label = top), color = "white", size = 3) +
theme(aspect.ratio=1,legend.position="top", legend.text=element_text(angle=90,vjust = 0.5, hjust=0.5),
legend.direction = "horizontal") +
scale_fill_gradient2(low = "white", high = "red") +
labs(y = "Time-lag period (months)",
x = "Rainfall period (months)")
plot(P)
png("plot MDB rain and outbreaks coef.png", width = 120, height = 90, units='mm', res = 600)
print(P)
dev.off()## png
## 2Rainfall and outbreaks with 12 month running mean
Monthly rainfall data is plotted in grey.
A right alligned rolling mean is plotted in blue, which means that it indicates the mean rainfall in the preceding 12 months.
Outbreaks are plotted as red triangles
The orange line is an index of outbreak probability based on the average predicted probability of the top models falling within 2 AIC units.
#calculate year value
I$Date <- I$Year+I$month/12
#add fitted values from best model as Expected Probabilities
I$ExpProb <- 1 / (1 + exp(-I$fit))
jitter <- position_jitter(width = 0, height = 5)
P <- ggplot(data=I, aes(x=Date)) +
theme_classic() +
geom_line(aes(y=rainfall),color="grey") +
geom_line(aes(y=rollmean(rainfall, 12, na.pad=TRUE,align="right")), color="blue")+
#geom_line(aes(y=rollmean(rainfall, 12, na.pad=TRUE,align="center")), color="green")+
xlim(1970,2021) +
labs(y = "Rainfall (mm)",
x = "")+
#geom_line(aes(y=ExpProb*1000-400), color="orange") +
geom_point(data=O, aes(x=Year+month/12, y=20), position=jitter, shape=2, color="red", size=2.5)
plot(P)
png("plot MDB rain and outbreaks.png", width = 120, height = 100, units='mm', res = 600)
print(P)
dev.off()## png
## 2