Multidimensional Classification of Examinees Using the Mixture Random Weights Linear Logistic Test Model

Abstract

An essential feature of the linear logistic test model (LLTM) is that item difficulties are explained using item design properties. By taking advantage of this explanatory aspect of the LLTM, in a mixture extension of the LLTM, the meaning of latent classes is specified by how item properties affect item difficulties within each class. To improve the interpretations of latent classes, this article presents a mixture generalization of the random weights linear logistic test model (RWLLTM). In detail, the present study considers individual differences in their multidimensional aspects, a general propensity (random intercept) and random coefficients of the item properties, as well as the differences among the fixed coefficients of the item properties. As an empirical illustration, data on verbal aggression were analyzed by comparing applications of the one- and two-class LLTM and RWLLTM. Results suggested that the two-class RWLLTM yielded better agreement with the empirical data than the other models. Moreover, relations between two random effects explained differences between the two classes detected by the mixture RWLLTM. Evidence from a simulation study indicated that the Bayesian estimation used in the present study appeared to recover the parameters in the mixture RWLLTM fairly well.