Variance of random effects in binomial lmer
Dear all, Why is the estimated variance of a random effect different from the variance of the predicted random effects in a lmer with logit link and binomially distributed errors?
mod <- lmer(y~(1|x), family=binomial)
Random effects: Groups Name Variance Std.Dev. x (Intercept) 7.1227 2.6688 Number of obs: 10000, groups: x, 500
var(ranef(mod)$x)
(Intercept) (Intercept) 5.126217 These two (variance of random effects and var(ranef(mod)$x)) are the same in a lmer with normally distributed errors and identity link. So what is the difference? Syntax to generate data: n1 <- 500 n2 <- 20 sd1 <- 3 sd2 <- 1 AA <- rnorm(n1, 0, sd1) BB <- list() for(i in 1:length(AA)) BB[[i]] <- AA[i]+rnorm(n2, 0, sd2) BB2 <- unlist(BB) y1 <- exp(BB2)/(1+exp(BB2)) y <- rbinom(length(y1), 1, y1) x <- factor(rep(1:n1, each=n2)) Thanks for your help Geir H. Bolstad PhD candidate, Biology Norwegian University of Science and Technology