The computation in the multinomial logit mixed effects model is costly especially when the response variable has a large number of categories, since it involves high-dimensional integration and maximization. Tsodikov and Chefo (2008) developed a stable MLE approach to problems with independent observations, based on generalized self-consistency and quasi-EM algorithm developed in Tsodikov (2003). In this paper, we apply the idea to clustered multinomial response to simplify the maximization step. The method transforms the complex multinomial likelihood to Poisson-type likelihood and hence allows for the estimates to be obtained iteratively solving a set of independent low-dimensional problems. The methodology is applied to real data and studied by simulations. While maximization is simplified, numerical integration remains the dominant challenge to computational efficiency. © 2010 Elsevier B.V. All rights reserved.
Wang, S., & Tsodikov, A. (2010). A self-consistency approach to multinomial logit model with random effects. Journal of Statistical Planning and Inference, 140(7), 1939–1947. https://doi.org/10.1016/j.jspi.2010.01.034