Modelling Repeated Categorical Responses

University Of Florida, Gainesville FL

Investigators

Abstract

This research will develop statistical methods for modeling and analyzing categorical responses having clustering, most commonly due to repeated measurement. The main focus is generalized linear mixed models and extensions for multinomial responses and for mixtures of categorical and continuous responses. The issues to be studied include (1) modeling repeated ordinal and nominal responses using a distribution-free approach for the random effects, (2) addressing related misspecification and efficiency issues, (3) extending standard models for association and conditional association to allow heterogeneity of odds ratios by using random effects in binomial logit and Poisson loglinear models, (4) incorporating a wide variety of random effects models for categorical responses in an extended class of generalized loglinear mixed models, and (5) modeling repeated measurement of multivariate responses that are mixtures of discrete and continuous responses using random effects. Related work includes modeling of repeated compositional data, developing summary measures for comparing non-nested models for handling repeated measurement data, developing improved small-sample confidence intervals for parameters summarizing repeated measurement data, and writing survey articles on topics related to modeling clustered, categorical data. This project will study and develop a type of model that is increasingly popular for applications in which standard statistical methods are inadequate because observations are not independent. The lack of independence occurs, for instance, when the same subjects are measured repeatedly over time or when observations occur in clusters such as families. The models are also useful for the study of subjects' opinions expressed on a battery of related questions in a survey -- for instance, opinion about whether government spending should increase, remain the same, or decrease, measured separately for defense, education, health, and the environment. This project will formulate new models, develop inferential methods for them, and illustrate them with social-science related data sets. Potential applications include comparing responses to similar questions on a survey, modeling survey questions in which respondents can select more than one outcome category, and summarizing how effects vary among groups that are sampled from some larger set of groups (e.g., schools, hospitals).