Jonathan Hartzel, University of Florida

Random Effects Models for Nominal and Ordinal Data

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 talk we will discuss random effects models for analyzing longitudinal or clustered nominal and ordinal response data. Specifically, we will 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. For both approaches, we will outline estimation algorithms for obtaining maximum likelihood estimates of the fixed parameters and of the random effects distribution. We then consider the application of the proposed models to ordinal response data arising from a multi-center clinical trial. In particular, we consider a heterogeneous association model in which both the center and center-by-treatment factors are consider random. We then propose an adaptive Gauss-Hermite approximated score test for testing that a common association holds for all centers.