The Multicomponent Latent Trait Model for Diagnosis

Abstract

Heterogeneous item content is prevalent on psychological and educational tests that measure global traits or competencies, such as general intelligence and achievement tests. In such tests, the domain is broadly defined, so as to include many attributes and skills. Items often vary substantially in both the type and the number of attributes or skills that are involved in item solving. A hierarchical organization is often necessary to accommodate the heterogeneity of the test domain. For example, the mathematical achievement tests that are routinely administered in all U.S. states at the end of the school year typically have this hierarchical structure. The multicomponent latent trait model for diagnosis (MLTM-D) was developed for application to heterogeneous tests. MLTM-D is a confirmatory model that permits diagnosis at broad and more specific attribute or skill levels. In the current study, MLTM-D is applied to diagnose mastery at both the broad and specific skill levels in middle school mathematics. MLTM-D is presented, and methods involved in application are described.