AN EXTENSION OF THE PARTIAL CREDIT MODEL WITH AN APPLICATION TO THE MEASUREMENT OF CHANGE

The partial credit model is considered under the assumption of a certain linear decomposition of the item x category parameters delta(in) into ''basic parameters'' alpha(j). This model is referred to as the ''linear partial credit model''. A conditional maximum likelihood algorithm for estimation of the alpha(j) is presented, based on (a) recurrences for the combinatorial functions involved, and (b) using a ''quasi-Newton'' approach, the so-called Broyden-Fletcher-Goldfarb-Shanno (BFGS) method; (a) guarantees numerically stable results, (b) avoids the direct computation of the Hesse matrix, yet produces a sequence of certain positive definite matrices B(k), k = 1, 2, . . . , converging to the asymptotic variance-covariance matrix of the alpha(j). The practicality of these numerical methods is demonstrated both by means of simulations and of an empirical application to the measurement of treatment effects in patients with psychosomatic disorders.