A self-consistency approach to multinomial logit model with random effects

• Published in: Journal of statistical planning and inference Vol. 140; no. 7; pp. 1939 - 1947
• Main Authors: Wang, Shufang, Tsodikov, Alex
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.07.2010
• Subjects: Multinomial logit model with random effects; QEM algorithm; Multinomial logit model with random effects; QEM algorithm
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2010.01.034

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.