| Applications in which data have clumps occur in many disciplines. In this dissertation, we develop methods for modeling a few special cases of this type of data, including repeated measures of zero-inflated count data, cross-sectional compliance data, and repeated measures of compliance data.;For count responses, the situation of excess zeros (relative to what standard models allow) often occurs in many biomedical and sociological applications. Modeling repeated measures of zero-inflated count data presents special challenges. We present two types of random effects models for repeated measurements on this type of response variable. The first model is a hurdle model with random effects, which separately handles the zero observations and the positive counts. In maximum likelihood model fitting, we consider both a normal distribution and a nonparametric approach for the random effects. We also discuss a special type of the hurdle model, which can be used to test the existence of zero-inflation. The second model is a cumulative logit model with random effects, which has the simplicity of using a single model to handle the zero-inflation problem. We illustrate the proposed methods with an example from an occupational injury prevention program.;For compliance data, there are two clumps, one at 0% and one at 100%. To analyze cross-sectional compliance data, we propose a two-part model, a cumulative logit model, and a quasi-likelihood method. Our emphasis is on the mixtures of experts model (ME). We apply the EM algorithm in fitting the ME model. Then, we extend these methods into the repeated measures settings. At the subject level, we propose a random effects ME model and use a nonparametric maximum likelihood method in model fitting. At the population level, we introduce the generalized estimating equation (GEE) method and extend it to the simplex distribution. Then we combine this extension of the GEE method with the ME model to form the mixtures of marginal models. A generalization of the EM algorithm, the ES algorithm is introduced to fit the mixtures of marginal models. We use two asthma medication compliance studies for illustration of our methods. |
