The purpose of the present study was to extend the model of measurement invariance by simultaneously estimating invariance across multiple populations in the dichotomous instrument case using multi-group confirmatory factor analytic and multiple indicator multiple causes (MIMIC) methodologies. Using the Arabic version of the General Aptitude Test (GAT), invariance was tested at the configural, metric, and scalar levels. Results indicated that the hybrid model that incorporates both the multi-group case and the MIMIC model provide a viable alternative to the measurement of invariance between variables when they interact. Metric and scalar invariance were supported for all of GAT's subscales with the exception of Word Meaning for which lack of invariance was likely caused by model misspecification. Subtle effects were observed in favor of public school testees, but they did not exceed significance levels.