Coauthor Sun-Joo Cho, Vanderbilt University

Based on the ARIP model, binary and ordered-category data on behaviors (as items) can be approached with mixed logistic models, containing random parameters for the persons and for the behaviors: a propensity parameter of the person, an induction parameter for how much the behavior is induced, and a sensitivity parameter for how sensitive the behavior is to the underlying propensity of the person. The induction and sensitivity parameters are each defined as a linear function of behavioral features and a random error term. Because the behaviors as well as the persons are treated as random effects, the ARIP model is a crossed random-effect model. Such models are difficult to estimate because integrals are involved which are not only intractable, but also high-dimensional. Two solutions are developed, a Bayesian approach and an alternating imputation posterior approach with adaptive quadrature (Cho & Rabe-Hesketh, 2009). The application to verbal aggression data shows, among other findings, that the inductive power is lower for doing than for wanting and that wanting has a higher degree of discrimination, and thus reflects better than doing the underlying propensity.