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A common theme in mental health services research is two-stage sampling i.e., sampling of responses within subjects and sampling of subjects within populations. For example, in prospective longitudinal studies subjects are repeatedly sampled and rated on measures of well being, mental and physical level of functioning, quality of life; and these subjects are sampled from a population, often stratified on the basis of type or amount of service utilization. Like all behavioral characteristics, these outcome measures exhibit individual differences. We should be interested in not just the mean trend, but in the distribution of these trends in the population of subjects. Then we can speak of the number or proportion of subjects who are functioning more or less positively, at such and such a rate. We can describe the behavioral relationship, not as a fixed law, but as a family of laws, the parameters of which describe the individual behavioral tendencies of the subjects in the population. This view of behavioral research leads inevitably to Bayesian methods of data analysis. The relevant distributions exist objectively and can be investigated empirically.

The purpose of this proposal is to further explore application of the empirical Bayesian theory of estimation in connection with common statistical problems encountered in mental health services research. Our previous work in this area has led to widespread use of random-effects regression models for the analysis of longitudinal mental health services data. This statistical model is a classic example of the empirical Bayesian approach to parameter estimation. Using this general theory of estimation, solutions are proposed for problems such as random-effects probit regression, full-information item factor analysis, and multivariate probit analysis. These models are critical to this emerging field in that they provide statistically rigorous approaches to both the definition and analysis of outcome which is invariably multidimensional and based on qualitative factors. The primary focus of this proposal is to further statistical development in these areas and disseminate this information to both statisticians and mental health services researchers in the form of scientific papers and computer software. Our previous grant and competitive renewal have led to the development of the MIXOR and MIXREG computer programs that are widely used by mental health services researchers in analysis of their longitudinal data.
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