| Models for nominal and ordinal response data are important in many areas of research. In medical studies, patients are often evaluated on an ordinal or graded scale. Nominal data, such as types of services used at a hospital, are frequent in the field of health care. It is often the case that such data are nested within clusters or repeatedly assessed over time. In this dissertation we propose random effects models for analyzing longitudinal or clustered nominal and ordinal response data. Specifically, we present a general multinomial logit random effects model that we motivate within the framework of a multivariate generalized linear mixed model. As special cases of the proposed model, we consider models based on the cumulative logit, adjacent-category logit, and continuation-ratio logit link functions for analyzing ordinal response data, and the baseline-category logit link function for nominal data.; For the proposed multinomial random effects models, we consider both parametric and nonparametric assumptions for the distribution of the random effects. In the parametric approach, we assume that the random effects follow a multivariate normal distribution. We consider direct maximization of the marginal likelihood using adaptive Gauss-Hermite quadrature, as well as indirect maximization using an automated Monte Carlo expectation-maximization (EM) algorithm. In addition, we propose a pseudo-likelihood approach for obtaining approximate maximum likelihood estimates. In the nonparametric approach, we assume that the random effects follow an unspecified discrete distribution. We propose an EM algorithm for obtaining nonparametric maximum likelihood estimates of the model parameters and the discrete distribution. Using simulation, we compare the performance of the parametric and nonparametric approaches when the random effects distribution is misspecified.; We also examine the use of the proposed models for modeling ordinal multi-center clinical trial data. We consider random effects models that allow for a common association across all centers, as well as heterogeneous associations. We also propose Laplace and adaptive Gauss-Hermite quadrature approximated score tests for testing that a common association parameter holds in the heterogeneous random effects model. We show that the latter test performs poorly for small to moderate numbers of centers. |
