df <- data.frame(Fibro=sample(x=c("Oui", "Non"), 1000, replace=TRUE), year=floor(runif(1000, min=2004, max=2010))-2000, ID=sample(x=1:100, 1000, replace=TRUE)) df2 <- cbind(df, FibroNum=as.numeric(df$Fibro=="Oui"), NonFibroNum=1-as.numeric(df$Fibro=="Oui")) df2$year <- df2$year + df2$FibroNum df2$Fibro <- as.factor(df2$Fibro) df2$ID <- as.factor(df2$ID) head(df2) library(lme4) These solutions are equivalent g1 <- glmer(formula = Fibro ~ year + (1 | ID), data=df2, family=binomial(link="logit")) g2 <- glmer(formula = FibroNum ~ year + (1 | ID), data=df2, family=binomial(link="logit")) g3 <- glmer(formula = cbind(FibroNum, NonFibroNum) ~ year + (1 | ID), data=df2, family=binomial(link="logit")) library(cAIC4) cAIC(g1) cAIC(g2) cAIC(g3)