The difference of chi-squared statistics between the measurement invariant model, in which measurement parameters (factor loadings and thresholds) are constrained equal between males and females, and the measurement noninvariant model was significant (Δχ2 = 305.425, Δdf = 124, p < 0.001). This can indicate that measurement parameters between the subgroups are not equivalent, and alcohol use and antisocial behavior were differentially measured in male and female participants. However, the chi-squared difference test is prone to type I error especially when sample size is this large. In addition, fit indices indicated that the measurement invariant model fit well to the data (CFI = 0.960, TLI = 0.961, RMSEA [90% CI] = 0.018 [0.017, 0.018]). In fact, the measurement invariant model fit slightly better than the measurement noninvariant model in terms of fit indices (CFI = 0.957, TLI = 0.957, RMSEA [90% CI] = 0.019 [0.018, 0.019]). Thus, in the following analyses, measurement parameters were constrained to be equal across the sexes to ensure equivalent measurement of alcohol use and antisocial behavior factors in male and female subgroups.
