A benefit of using the multifaceted Rasch model is the ability to factor out or control for confounding factors in the estimation of person ability and item difficulty. This study experiments with a variation of the multifaceted Rasch analysis in calibrating the effects of demographic characteristics that are intended to overcome the problem of overparameterized person measures. The sample consisted of 1,319 U.S. eighth graders who participated in the Second International Mathematics Study (SIMS). The instrument was a seven-item measure of student effort taken from a questionnaire developed for the SIMS. In attempting to calibrate effects of the demographic characteristics, the FACETS program was not able to determine how much of person ability was due to the individual and how much was due to the gender or the racial/ethnic category. The proposed variation reverses the order in which the facets are calibrated, determines the gender and racial/ethnic effects and allocates the residual to person ability. This approach produces unambiguous person measures and, for these data, appears to make adjustments to the person measures for individuals based on their group membership. Two tables present study findings, and an appendix describes the variables. (Contains 5 references.) (SLD)