People differ enormously in many physical and behavioral characteristics. Height and weight are physical differences; lifestyle variables, such as occupational, hobby, or recreational activities are behavioral differences. These differences are typically observed, but many differences are not directly observable, such as beliefs, attitudes, or the ways by which people perceive the world. To understand these unobservable differences it is necessary to infer qualities of these differences through observations which we can make. An often useful vehicle for doing so employs statistical theory called finite mixtures. This approach is based on two central ideas. One is that differences in unobservables can be viewed as relatively distinct classes in the same way one might view physical differences: righthanded or left, male or female. The other central notion is to make these differences in unobservable classes equivalent to different probability distributions. As an example, suppose the heights of 100 randomly selected adults were measured. The goal is to estimate the heights of men and women. Suppose however, there was a failure to code the measurements for sex. It is still possible to estimate the mean heights of each sex, the proportions of males and females in the population, and the probability that an individual measurement is from a man or a women. The reason this can be done is because the probability distributions for height are different: Men and women differ in their average height, which means they have different probability distributions for height.
This research will use analytical, empirical, and computer methods to develop finite mixture models that make weaker assumptions than standard mixture theory. Some of the approaches are nearly nonparametric in the sense that the unobserved probability distributions need not be fully specified. In particular, three of the five projects will explore the binomial mixture approach. The other two projects will examine other largely distribution free mixture strategies not tied to the binomial. The models to be developed should make it easier to identify important unobserved features of individuals such as those 'at risk' for certain personality disorders thereby anticipating, in the future, possible intervention strategies to facilitate development.
|Effective start/end date||8/15/01 → 7/31/05|
- National Science Foundation: $299,980.00