Comparison of Partially Measured Latent Traits across Nominal Subgroups

Abstract

Abstract This article presents a method for estimating the subgroup distributions of a latent trait measured as a normal variate in the population. This problem occurs in large-scale assessments, such as the National Assessment of Educational Progress, the National Adult Literacy Survey, and other programs where proficiencies are estimated via marginal maximum likelihood through a model based on item-response theory. Heretofore, estimates of subgroup means were often estimated using ad hoc assumptions about within-group distributions, which conflicted with concurrent assumptions about normality of the population distributions. The method presented here removes the conflict, using consistent distributional assumptions for population and subgroup estimates.