Our data set consists of a matrix with a few thousand respondents (rows), many items of ten surveys (columns), and all 0’s and 1’s for a certain survey answering behaviour (either responding ‘I don’t know’ (=1) or not (=0)), that is, a 1 or 0 for every filled out item for each survey. We use the package lme4, the function glmer, and the binomial family logit, with a cross-classified logistic multilevel analysis for an intercepts-only model to estimate the variances of 1) the random intercept for respondent, 2) the random intercept for survey, and 3) the random intercept for respondent-survey interaction (we do not use predictors/fixed effects so far).
We have several of these data sets/answering behaviours to analyze separately and we find seemingly plausible variances for the three random intercepts concerning all answering behaviours (between 0.0 and 4.6), without warnings/errors given by R. In most cases, many respondents (about half and sometimes even more than half of them) only score 0’s for all items and surveys they filled out, and in some cases, also a smaller but substantial part of them only scores 1’s for all items and surveys.
My questions: How does lme4/glmer calculate the variances of the random intercepts for these cross-classified random effects intercepts-only models using the logit? To what extent can these be fully trusted in the (our) case of having so many exact 0’s (and some exact 1’s)?
