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Blog post on random effects in mixed models
library(lme4)
library(ggplot2)
#create some levels
levs <- as.factor(c("l1","l2","l3","l4","l5"))
#set the factor means
f_means <- c(6,16,2,10,13)
# set individual as a factor
ind <- as.factor(paste("i",1:9,sep=""))
#Set individual effects
i_eff <- seq(-4,4,length=9)
#now let's simulate a repeated measure for each individuals
idf <- data.frame(matrix(0,ncol=3,nrow=45))
colnames(idf) <- c("size","ind","levs")
counter <- 1
for(i in 1:length(levs)){
for(j in 1:length(ind)){
idf$size[counter] <- rnorm(1,f_means[i]+i_eff[j],.3)
idf$ind[counter] <- ind[j]
idf$levs[counter] <- levs[i]
counter <- counter + 1
}
}
idf$ind <- rep(ind,5)
idf$levs <- sort(rep(levs,9))
ggplot(idf,aes(x=levs,y=size,group=ind,colour=ind))+geom_point()+geom_path()
m3 <-lmer(size~levs - 1 +(1|ind), data=idf)
## Now let's randomize the individuals
idf_rand <- idf
for(i in 1:5){
idf_rand$ind[idf_rand$levs==levs[i]] <- sample(idf$ind[idf$levs==levs[i]],9,replace=F)
}
# here we can visualize the data and examine individual effects
ggplot(idf_rand,aes(x=levs,y=size,group=ind,colour=ind))+geom_point()+geom_path()
#Fit the model and then check the variance term
m4 <-lmer(size~levs - 1 +(1|ind), data=idf_rand)
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