GLMM with binomial

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)

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