Mixture modeling with behavioral data

United States schools and students suffer from problems associated with student behavioral disorders. There is a need for innovate statistical methods to analyze data to which will help inform the development of new strategies to deal with the issues associated with behavioral problems. The three papers in this dissertation focus on explicating certain mixture models which have shown promise in analyzing behavioral data. An important interest in mixture modeling is the investigation of what types of individuals belong to each latent class by relating classes to auxiliary variables. The first paper presents results from real data examples and simulations to show how various factors, such as sample size, can impact the estimates and standard errors of auxiliary variable effects and testing mean equality across classes. Based on the results of the examples and simulations, suggestions are made about how to select auxiliary variables for a latent class analysis (LCA). The second paper discusses the factor mixture model (FMM) which uses a hybrid of both categorical and continuous latent variables.;The FMM is a good model for the underlying structure of behavioral disorders because the use of both categorical and continuous latent variables allows the structure to be simultaneously categorical and dimensional. The use of the FMM in behavioral research is not prevalent because there is little research about how the FMM should be applied in practice. This paper explores the FMM by studying two real data examples: conduct disorder and attention-deficit hyperactivity disorder. Through these examples, this paper aims to explain the different formulations of the FMM, the various steps in building a FMM, as well as how to decide between a FMM and alternative models. The third paper explores of the use of two mixture model as potential phenotypes in ACE analysis: LCA and FMM. The use of these models as phenotypes is demonstrated through an example concerning conduct disorder in a sample of Finnish twins. A discussion about extending the models in this dissertation to be applicable to longitudinal data or include gene by environment (GxE) interactions is also presented.