期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2019
页码：1-34
DOI：10.1007/s13171-019-00168-1
出版社：Indian Statistical Institute
摘要：Regression models for multinomial responses with time dependent covariates have been studied recently both in longitudinal and time series setup. For practical importance, in this paper, we focus on a longitudinal multinomial response model with two categorical covariates to study their main and interaction effects after accommodating a lag 1 dynamic relationship between past and present multinomial responses. The proposed model could be generalized easily to accommodate multiple (more than two) categorical covariates and their interactions. As far as the estimation of the regression and the dynamic dependence parameters is concerned, we follow a recent parameter dimension-split based approach suggested by Sutradhar ( Sankhya A 80 , 301–329 2018 ) but unlike the conditional method of moments (CMM) used in this study, we use a more efficient estimation approach, namely the so-called conditional generalized quasi-likelihood (CGQL) method for the estimation of the dynamic dependence parameters. The regression parameters are also estimated by using the same CGQL approach where responses become independent conditional on the past responses which is similar in principle to the likelihood estimation where the likelihood function is formed as a product of transitional probabilities conditional on the past responses. The asymptotic properties of the CGQL estimators are provided in details. The higher efficiency performance of the CGQL approach over the CMM approach is also demonstrated, for example, for the estimation of the dynamic dependence parameters.
关键词：Asymptotic properties ; Covariates with possible interactions ; Dynamic dependence parameters ; Conditional generalized quasi-likelihood estimation ; Lag 1 transitional multinomial probabilities ; Unconditional method of moments
