Item bias detection using the loglinear Rasch model: Observed and unobserved subgroups

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 x test score x item 1 x ... x item k contingency table. If the subgroup membership is unknown, the models are the incomplete-latent-class models of S. J. Haberman (1979). The (conditional) Rasch model is formulated as a quasi-loglinear model. The parameters in this 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. An example uses data from a test taken by 286 Dutch undergraduates who took a multiplication test using Roman numerals and numbers written out in Dutch. Some of the examinees had received training in multiplying Roman numerals. It was expected that Roman items would be biased, and the procedure confirmed this bias. Five tables present the models and study data