Loglinear-latent-class models for detecting item bias

The use of loglinear latent class models to detect item bias was studied. Purposes of the study were to: (1) develop procedures for use in assessing item bias when the grouping variable with respect to which bias occurs is not observed; (2) develop bias detection procedures that relate to a conceptually different assessed trait--a categorical attribute; and (3) exemplify the use of these developed procedures with real world data. Models are formulated so that the attribute to be measured may be continuous, as in a Rasch model, or categorical, as in latent class models. The item bias to be studied may correspond to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of bias are described. These methods are illustrated through analysis of a "real world" data set from a study of multiplication items administered to 286 Dutch undergraduates. Bias was related to a manifest grouping variable by giving 143 of the subjects some training in Roman numerals, in which some of the multiplication problems were written. Results indicate that it was possible to explain item bias through differences in item difficulties or error rates across levels of grouping variables. The model represented can be extended to include several observed and unobserved variables. Ten tables present information about the models and findings of the study.