Henk Kelderman

Loglinear multidimensional IRT models for polytomously scored items

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.

Item bias detection using loglinear irt

A method is proposed for the detection of item bias with respect to observed or unobserved subgroups. The method uses quasi-loglinear models for the incomplete subgroup × test score × Item 1 × ... × itemk contingency table. If subgroup membership is unknown the models are Habermans incomplete-latent-class models.The (conditional) Rasch model is formulated as a quasi-loglinear model. The parameters in this loglinear model, that correspond to the main effects of the item responses, are the conditional estimates of the parameters in the Rasch model. Item bias can then be tested by comparing the quasi-loglinear-Rasch model with models that contain parameters for the interaction of item responses and the subgroups.

Computing Maximum Likelihood Estimates of Loglinear Models from Marginal Sums with Special Attention to Loglinear Item Response Theory.

In this paper algorithms are described for obtaining the maximum likelihood estimates of the parameters in loglinear models. Modified versions of the iterative proportional fitting and Newton-Raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table. This is desirable if the contingency table becomes too large to store. Special attention is given to loglinear IRT models that are used for the analysis of educational and psychological test data. To calculate the necessary expected sufficient statistics and other marginal sums of the table, a method is described that avoids summing large numbers of elementary cell frequencies by writing them out in terms of multiplicative model parameters and applying the distributive law of multiplication over summation. These algorithms are used in the computer program LOGIMO. The modified algorithms are illustrated with simulated data.

Examining differential item functioning due to item difficulty and alternative attractiveness

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.

Common Item Equating Using the Loglinear Rasch Model

A method is proposed to equate different sets of items administered to different groups of individuals using the Rasch model. A Rasch equating model is formulated that describes one common Rasch scale in different groups with different but overlapping sets of items. The item parameters can then be estimated simultaneously, avoiding different parameter estimates of common items in different groups. The model can be tested globally to test the hypothesis of one common Rasch scale, and the goodness of link can be tested. The method is based on the quasi-loglinear Rasch model.