The purpose of this research study was to assess item response model-test data fit using residuals. First, a comparison of raw and standardized residuals for describing model-test data fit was carried out. Second, hypotheses concerning the relationship between residual sizes and several item characteristics were studied. The analyses with residuals were carried out with NAEP mathematics test data using the one-, two-, and three-parameter logistic test models. The results from the investigation highlighted clearly the advantages of addressing the question of model-test data fit with residuals. (Author)