title: A Self-consistency Approach to Multinomial Logit Model with Random Effects.
abstract: 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.
authors.affiliation: Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
authors.forename: Shufang
authors.initials: S
authors.lastname: Wang
authors.forename: Alex
authors.initials: A
authors.lastname: Tsodikov
references.citation: Stat Med. 2003 May 15;22(9):1433-46
references.pmid: 12704607
references.citation: J Stat Plan Inference. 2008;138(8):23802397
references.pmid: 18709183
references.citation: Comput Methods Programs Biomed. 2007 Sep;87(3):262-9
references.pmid: 17686544
references.citation: J R Stat Soc Series B Stat Methodol. 2003 Aug 1;65(3):759-774
references.pmid: 21127741
references.citation: Biostatistics. 2002 Sep;3(3):347-60
references.pmid: 12933602
references.citation: Stat Med. 1997 Oct 30;16(20):2311-25
references.pmid: 9351167