Abstract
The partial credit model is considered under the assumption of a certain linear decomposition of the item × category parametersδ ih into “basic parameters”α j. This model is referred to as the “linear partial credit model”. A conditional maximum likelihood algorithm for estimation of theα 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 matricesB k ,k=1, 2, ..., converging to the asymptotic variance-covariance matrix of the\(\hat \alpha _j \). 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.
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The authors thank one anonymous reviewer for his constructive comments. Moreover, they thankfully acknowledge financial support by the Österreichische Nationalbank (Austrian National Bank) under Grant No. 3720.
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Fischer, G.H., Ponocny, I. An extension of the partial credit model with an application to the measurement of change. Psychometrika 59, 177–192 (1994). https://doi.org/10.1007/BF02295182
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DOI: https://doi.org/10.1007/BF02295182