# Correlated Random Effects Probit vs. GEE Population-Averaged Probit

My question relates to recent work on correlated random effects probit models (see these slides from Wooldridge) and comparing them to GEE population averaged probit models: Is one approach better as accounting for within-subject correlations than the other?

CRE (more mixed effect?) models account for within-subject variation by including a within-subject variable ($\bar{x}_{i}$) capturing the mean of each time-variant explanatory variable ($x_{it}$). The statistical significance of this parameter is then a test of traditional RE assumption that the individual effects are independent of the explanatory variables. It also serves as a correction for violations of this assumption, but requires (I think) assuming that the individual effect is normally distributed around the mean of the individual's values.

In GEE models, from what I understand, within subject correlations are accounted for via the correlation structure of the error term. What I don't quite understand is if/why the betas are not affected by within-subject correlations and the extent to which we need to worry about that.

I understand that GEEs can't recover the individual effect, but I don't follow why much of the action is in the errors and there is little discussion of how within-subject variation might bias the population estimate of the betas.