Using explanatory item response models to analyze group differences in science achievement

This article illustrates the use of an explanatory item response modeling (EIRM) approach in the context of measuring group differences in science achievement. The distinction between item response models and EIRMs, recently elaborated by De Boeck and Wilson (2004), is presented within the statistical framework of generalized linear mixed models. It is shown that the EIRM approach provides a powerful framework for both a psychometric and statistical analysis of group differences. This is contrasted with the more typical two-step approach, in which psychometric analysis (i.e., measurement) and statistical analysis (i.e., explanation) occur independently. The two approaches are each used to describe and explain racial/ethnic gaps on a standardized science test. It is shown that the EIRM approach results in estimated racial/ethnic achievement gaps that are larger than those found in the two-step approach. In addition, when science achievement is examined by subdomains, the magnitude of racial/ethnic gap estimates under the EIRM approach are more variable and sensitive to the inclusion of contextual variables. These differences stem from the fact that the EIRM approach allows for disattenuated estimates of group level parameters, whereas the two-step approach depends on estimates of science achievement that are shrunken as a function of measurement error.