NSF DMS-9705032 Latent variable models in action: hierarchical Bayes and mixture models for repeated discrete measures with individual differences Brian Junker Carnegie Mellon University PROJECT ABSTRACT: A central feature of this research is the development of widely applicable methodology for latent variable models for measurement problems in education, psychology and the social sciences. This methodology is being developed and tested in several specific areas: Monotonicity and stochastic ordering properties that follow from the strictly unidimensional latent variable representation are being studied and applied to nonparametric scaling problems. A promising Markov chain Monte Carlo method is being extended and applied to a variety of problems, including: correct modeling of rater variability in educational achievement data; accomodating heterogeneous catchability in multiple-recapture censuses; and developing methods for multidimensional and hierarchical latent variable models for discrete repeated measures. In addition, the research addresses the sensitivity of inferences to underspecification of the model. A second thrust of the research is to refine and develop existing characterizations of unidimensional latent structure into a statistical theory of, and statistical methods for assessing, latent variable dimensionality. This work aims to more fully blend psychometric and statistical approaches to latent variable models for repeated discrete measures. Psychometric methodology tends to concentrate on model building and model features; and psychometric data analysis tends toward issues of scaling (selecting questions that ``hang together'' in the sense that a unidimensional latent variable model holds), reliability (ensuring that the latent variable can be estimated well from the questions selected), and the assessment of latent variable dimensionality from data. Statistical methodology tends to sidestep these bas ic psychometric questions, and instead concentrates on finer model adjustments, and various inferential and predictive tasks. The focus of this research is on statistical and psychometric features of latent variable models for repeated measures data, which is of interest to quantitative psychologists, educational measurement specialists, and cognitive scientists, as well as other social scientists. Much of the work is collaborative in nature, and it is built around the development of theory and methodology motivated from, and useful for, substantive applications.
