Generalized Dimensionality Assessment for Multidimensional Psychometric Models

This project developed statistical procedures for conducting dimensionality analysis in the context of multidimensional item response theory that are generalizable to a broad class of related latent variable statistical models. Psychometric models are motivated by the fact that what is of most interest cannot be directly observed and so use latent variables to represent constructs. Observed variables then serve as indicators of the underlying constructs. Popular item response theory (IRT) and related models typically structure the observable variables (i.e., scored item responses) as stochastically dependent on the latent variables. Unidimensional models in which a single latent variable underlies a set of observable variables have been predominantly employed in practice. Multidimensional models, in which two or more latent variables may be related and may underlie some of the same observable variables, have been developed to address theories that multiple skills or proficiencies are brought to bear in responding to observable items. The combination of Bayesian modeling strategies and modern computational capabilities have facilitated the estimation of complex, multidimensional models and with their emergence comes the need for appropriate model checking and model criticism procedures. Past work has shown that a model with an improperly specified dimensional structure may lead to (a) incorrect estimates of the values of variables; (b) incorrect estimates of the precision of the estimates; and (c) associated errors concerning (1) estimates of information and measurement precision; (2) linking of latent scales; (3) constructing measures and instruments; and (4) the interpretations of the latent variables and the inferences and decisions based on the model.