The goal of this project is to develop a theory for nonparametric, multidimensional, item-level measurement. The investigator's approach to multidimensional modeling relies on two recent advances in measurement: the submodel theorem and ForScore. The submodel theorem asserts that smooth multidimensional measurement models have equivalent unidimensional submodels. ForScore, a suite of unidimensional model fitting programs, provides means for fitting various unidimensional models that are equivalent to the smooth multidimensional models. The project will result in a set of computer programs for implementing the theory and a demonstration application of the theory in counseling psychology. Latent variable models are used in physical, biological, and social sciences. Multivariate latent variable modeling is less well developed than univariate modeling. If the project is successful, more complex and accurate applications of latent variable models will quickly become possible because researchers will be able to reduce problems involving many variables to univariate problems. For example, consider the analysis of gender differences. Men and women on average respond differently to questions of vocational choices. This research will allow the application of powerful unidimensional differential item functioning measures to be used in the two-dimensional domain of vocational choice. The analysis will increase our understanding of the etiology of gender differences in vocational choice and assist in the design of instruments that will be more useful to women.
