Some Applications of Logistic Latent Trait Models with Linear Constraints on the Parameters

Abstract

The linear logistic test model (LLTM), a Rasch model with linear constraints on the item parameters, is described. Three methods of parameter estimation are dealt with, giving special consideration to the conditional maximum likelihood approach, which provides a basis for the testing of structural hypotheses regarding item difficulty. Standard areas of application of the LLTM are surveyed, including many references to empirical studies in item analysis, item bias, and test construction; and a novel type of application to response-contingent dynamic processes is presented. Finally, the linear logistic model with relaxed assumptions (LLRA) for measuring change is introduced as a special case of an LLTM; it allows the characterization of individuals in a multidimensional latent space and the testing of hypotheses regarding effects of treatments.