When repeated binary responses along with time dependent covariates are collected over a short period of time from the members of a large number of independent families, there exits a well developed binary dynamic mixed logit (BDML) model to analyze such familial longitudinal binary data. As far as the inferences are concerned, this BDML model has been fitted by using the generalized quasi-likelihood (GQL) and the well known maximum likelihood (ML) methods. There are however situations in practice where categorical/multinomial responses with more than two categories are repeatedly collected from all members of the family. However, the analysis for this type of familial longitudinal multinomial data is not adequately addressed in the literature. We offer two main contributions in this paper. First, for the analysis of familial longitudinal multinomial data, we propose a multinomial dynamic mixed logit (MDML) model as a generalization of the BDML model and derive the basic properties such as non-stationary mean, variance and correlations for the repeated multinomial responses. Next, to understand these basic properties, we develop step by step likelihood estimating equations for the parameters involved in these properties. The relative asymptotic efficiency performance of the ML and GQL approaches is examined through a simulation study based on repeated binary responses, for example, from a large number of independent families each consisting of two members, causing both familial and longitudinal correlations. Also, a real life example on repeated multinomial data analysis is considered as an illustration.
Categorial responses Dynamic mixed models Familial correlations through random effects Longitudinal correlations through dynamic relationships Multinomial logit model
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The authors thank the audience of the symposium and a referee for their comments and suggestions.
Breslow, N., Clayton, D.G.: Approximate inference in generalized linear mixed models. J. Am. Stat. Assoc. 88, 9–25 (1993)zbMATHGoogle Scholar
Chen, B., Yi, G.Y., Cook, R.: Likelihood analysis of joint marginal and conditional models for longitudinal categorical data. Can. J. Stat. 37, 182–205 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
Conaway, M.R.: Analysis of repeated categorical measurements with conditional likelihood methods. J. Am. Stat. Assoc. 84, 53–62 (1989)MathSciNetCrossRefGoogle Scholar
Crowder, M.: On the use of a working correlation matrix in using generalized linear models for repeated measures. Biometrika 82, 407–410 (1995)CrossRefzbMATHGoogle Scholar
Fienberg, S.E., Bromet, E.J., Follmann, D., Lambert, D., May, S.M.: Longitudinal analysis of categorical epidemiological data: a study of three mile island. Environ. Health Perspect. 63, 241–248 (1985)CrossRefGoogle Scholar
Lipsitz, S.R., Kim, K., Zhao, L.: Analysis of repeated categorical data using generalized estimating equations. Stat. Med. 13, 1149–1163 (1994)CrossRefGoogle Scholar
Sutradhar, B.C., Farrell, P.J.: On optimal lag 1 dependence estimation for dynamic binary models with application to asthma data. Sankhya B 69, 448–467 (2007)MathSciNetzbMATHGoogle Scholar
Sutradhar, B.C., Rao, R.P., Pandit, V.N.: Generalized method of moments versus generalized quasi-likelihood inferences in binary panel data models. Sankhya B 70, 34–62 (2008)zbMATHGoogle Scholar
Ten Have, T.R., Morabia, A.: Mixed effects models with bivariate and univariate association parameters for longitudinal bivariate binary response data. Biometrics 55, 85–93 (1999)CrossRefzbMATHGoogle Scholar