Logistic latent trait models with linear constraints

Two linearly constrained logistic models which are based on the well-known dichotomous Rasch model, the ‘linear logistic test model’ (LLTM) and the ‘linear logistic model with relaxed assumptions’ (LLRA), are discussed. Necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived. Methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned.