Conditional fixed-effects logistic model

Estimating fixed effects in multilevel generalized linear models is challenging. This is because increasing the number of clusters (e.g., firms, persons) also increases the number of cluster-level fixed effects that need to be estimated. This is called the incidental parameter problem, and it invalidates the proof that maximum likelihood estimation produces consistent estimates. This is because the presence of cluster means in the model means that when the sample size approaches infinity, so does the number of model parameters.

Conditional logistic fixed effects regression is one workaround to this problem. The conditional logistic regression model assumes that just one observation (or alternatively any other constant number) in each cluster receives a 1 and others receive a 0. This model is useful, for example, for various problems that involve selecting one observation among many alternatives. The lecture explains the problem that conditional fixed effects addresses, how conditional fixed effects logistic regression estimate can be interpreted by calculating predictions or by plotting, and concludes with a simulation that demonstrates why fixed effects are needed. At the end, the conditional fixed effect logistic regression is compared to the linear fixed effects regression model, which is a simpler and useful alternative for many research problems.

Link to the slides: https://osf.io/n7mgu