I have a dataset with 8000 clusters and 4 million observations. Unfortunately my statistical software, Stata, runs rather slowly when using its panel data function for logistic regression:
xtlogit, even with a 10% subsample.
However, when using the nonpanel
logit function results appear much sooner. Therefore I may be able to benefit from using
logit on modified data that accounts for fixed effects.
I believe this procedure is coined the "Mundlak fixed effects procedure" (Mundlak, Y. 1978. Pooling of Time-Series and Cross-Section Data. Econometrica, 46(1), 69-85.)
I found an intuitive explanation of this procedure in a paper by Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. (2010). On making causal claims: A review and recommendations. The Leadership Quarterly, 21(6). 1086-1120. I quote:
One way to get around the problem of omitted ﬁxed effects and to still include Level 2 variables is to include the cluster means of all Level 1 covariates in the estimated model (Mundlak, 1978). The cluster means can be included as regressors or subtracted (i.e., cluster-mean centering) from the Level 1 covariate. The cluster means are invariant within cluster (and vary between clusters) and allow for consistent estimation of Level 1 parameters just as if ﬁxed-effects had been included (see Rabe-Hesketh & Skrondal, 2008).
Therefore cluster-mean centering seems ideal and practical for solving my computational problem. However, these papers seem to be geared towards linear regression (OLS).
Is this method of cluster-mean centering also applicable for "replicating" fixed effects binary logistic regression?
A more technical question that should result in the same answer would be: is
xtlogit depvar indepvars, fe with dataset A equal to
logit depvar indepvars with dataset B when dataset B is the cluster-mean centered version of dataset A?
An added difficulty I found in this cluster-mean centering is how to cope with dummies. Because dummies are either 0 or 1, are they identical in random and fixed effects regression? Should they not be "centered"?