# How to report variance components of random intercept model?

I have used: model1 <- glmer(binary~ X1 + X2 +(1|MAINCATEGORY/YEAR), data = mydata, family = binomial(link = 'logit')

To get the variance components of the model I used:

as.data.frame(VarCorr(model1)) and I get:

I know it is a very basic question, but how should I report the random intercept for the variables? For example for the variable YEAR What should I report in my results table? What is the standard error? How is it different from reporting a regular intercept? Should I report something like:

.38 (0.159)

The variance components refer to the estimated variance(s) of the random intercept(s). In your case, it appears you have a three level model, with observations nested within year nested within MainCategory. The as.data.frame(VarCorr(model1)) command gives you the variance estimates (components) of interest. In terms of reporting anything beyond the variance estimate itself (e.g., 0.038 for YEAR:MainCategory), I suggest consulting this thread on whether and how to report standard errors for random effect variance estimates.
• In generalized linear mixed models and because of the non-linear link function the interpretation is more complicated. I.e., the fixed-effect intercept of the model has the interpretation of log odds when X1 and X2 are zero, but also the random effect is zero. I.e., it is the log-odds for the average subject; however, note that this is not the average log odds over subjects. For more info on this, have a look here: stats.stackexchange.com/questions/365907/… – Dimitris Rizopoulos Jul 31 at 20:26