Exact Solutions for Irt Latent Regression Slopes and Latent Variable Intercorrelations
Using the factor analytic version of item response theory (IRT) models, estimates of the correlations between the latent variables measured by test items and correlations between observed covariates and IRT latent variables are derived. Themethods derived here can be applied to dichotomous items, polytomous items, or mixtures of both of these types of item. The estimates are simple in form and entail IRT item a-values (see below) and tetrachoric or biserial correlations-for dichotomous items-and IRT item a-values and polychoric or polyserial correlations for polytomous items ormixed-pairs of polytomous and dichotomous items. Applications are illustrated for:
1. Latent variable correlations underlying pairs of items or pairs of tests; and 2. Estimating slopes in latent variable regression problems.