Mixed-effects models for mental health services research

A common theme in mental health services research is multi-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 to Bayesian methods of data analysis. The purpose of this paper is to explore application of mixed-effects regression models to common statistical problems encountered in mental health services research. Previous work in this area has led to widespread use of mixed-effects regression models for the analysis of longitudinal mental health services data. Generalizations of the model lead to mixed-effects probit and logistic regression for binary, ordinal and nominal response data, full-information item factor analysis, and multivariate generalizations of probit analysis. These models are critical to mental health services research in that they provide statistically rigorous approaches to both the definition and analysis of outcome which is invariably multidimensional and based on qualitative factors.