Multicomponent latent trait models for complex tasks

Contemporary views on cognitive theory (e.g., Sternberg and Perez, 2005) regard typical measurement tasks, such as ability and achievement test items, multidimensional, rather than unidimensional. Assessing the levels and the sources of multidimensionality in an item domain is important for item selection as well as for item revision and development. In this paper, multicomponent latent trait models (MLTM) and traditional multidimensional item response theory models are described mathematically and compared for the nature of the dimensions that can be estimated. Then, some applications are presented to provide examples of MLTM. Last, practical estimation procedures are described, along with syntax, for the estimation of MLTM and a related model.