Implementation of a multinomial logit model with fixed effects

Abstract

Fixed-effect models have become increasingly popular in the field of sociology. The possibility of controlling for unobserved heterogeneity makes these models a prime tool for causal analysis. As of today, fixed-effects models have been derived and implemented for many statistical software packages for continuous, dichotomous, and count-data dependent variables, but there are still many important and popular statistical models, for which only population-average estimators are available, such as models for multinomial categorical dependent variables. In a seminal paper by Chamberlain (1980) such a model was derived. Possible applications would be analyses of effects on employment status with special consideration of part-time or irregular employment and analyses of the effects on voting behavior that impicitly control for longtime party identification rather than having to measure it directly. This model has not yet been implemented in any statistical software package. In this presentation, I show a first version of an ado-file, that closes this gap. The implementation draws on the native Stata multinomial logit and conditional logit model implementations. The actual ml evaluator utilizes Mata functions to implement the conditional likelihood function. To show the numerical stability and computational speed of the implementation, comparison results with the built-in clogit are shown, as well as some basic results with simulated data.