The use of new extension of standard Item Response Theory (IRT) modeling of dichotomous items to include external variables is proposed. External variables may appear both as categorical grouping variables and as continuous variables; this requires the formulation of a model for the relationships between the external variables and the response items. The methodology is illustrated in the context of educational achievement test data from the Second International Mathematics Study (SIMS). Students' responses to algebra items administered at the end of the eighth grade are related to external variables in the form of background variables measured at the beginning of the eighth grade. The resulting structural model--multiple indicators and multiple causes--(MIMIC) addresses the estimation of IRT item measurement parameters, assessment of the strengths of hypothesized antecedents to the student's latent trait level, detection of item bias (differential item performance), and testing and relaxation of IRT requirements of unidimensionality and conditional independence. The model also encompasses the LISREL formulation of K. G. Joreskog. With the SIMS data, the model proved useful particularly where there was an interest in post-test responses and where pre-test data were available. (TJH)