R. Prabhakar Rao

Longitudinal Mixed Models with t Random Effects for Repeated Count and Binary Data

Unlike the estimation for the parameters in a linear longitudinal mixed model with independent t errors, the estimation of parameters of a generalized linear longitudinal mixed model (GLLMM) for discrete such as count and binary data with independent t random effects involved in the linear predictor of the model, may be challenging. The main difficulty arises in the estimation of the degrees of freedom parameter of the t distribution of the random effects involved in such models for discrete data. This is because, when the random effects follow a heavy tailed t-distribution, one can no longer compute the basic properties analytically, because of the fact that moment generating function of the t random variable is unknown or can not be computed, even though characteristic function exists and can be computed. In this paper, we develop a simulations based numerical approach to resolve this issue. The parameters involved in the numerically computed unconditional mean, variance and correlations are estimated by using the well known generalized quasi-likelihood (GQL) and method of moments approach. It is demonstrated that the marginal GQL estimator for the regression effects asymptotically follow a multivariate Gaussian distribution. The asymptotic properties of the estimators for the rest of the parameters are also indicated.

Regression Models for Ordinal Categorical Time Series Data

Regression analysis for multinomial/categorical time series is not adequately discussed in the literature. Furthermore, when categories of a multinomial response at a given time are ordinal, the regression analysis for such ordinal categorical time series becomes more complex. In this paper, we first develop a lag 1 transitional logit probabilities based correlation model for the multinomial responses recorded over time. This model is referred to as a multinomial dynamic logits (MDL) model. To accommodate the ordinal nature of the responses we then compute the binary distributions for the cumulative transitional responses with cumulative logits as the binary probabilities. These binary distributions are next used to construct a pseudo likelihood function for inferences for the repeated ordinal multinomial data. More specifically, for the purpose of model fitting, the likelihood estimation is developed for the regression and dynamic dependence parameters involved in the MDL model.

On efficient inferences in familial-longitudinal binary models with two variance components

When a generalized linear mixed model (GLMM) with multiple (two or more) sources of random effects is considered, the inferences may vary depending on the nature of the random effects. For example, the inference in GLMMs with two independent random effects with two distinct components of dispersion will be different from the inference in GLMMs with two random effects in a two factor factorial design set-up. In this paper, we consider a familial-longitudinal model for repeated binary data where the binary response of an individual member of a family at a given time point is assumed to be influenced by the past responses of the member as well as two but independent sources of random family effects. For the estimation of the parameters of the proposed model, we discuss the well-known maximum-likelihood (ML) method as well as a generalized quasi-likelihood (GQL) approach. The main objective of the paper is to examine the relative asymptotic efficiency performance of the ML and GQL estimators for the regression effects, dynamic (longitudinal) dependence and variance parameters of the random family effects from two sources.