The configural invariance model, in which the factor loadings and thresholds were estimated freely for each group, had a good fit (χ2 (21) = 19.84, p = 0.531; RMSEA = 0.001). Constraining the factor loadings and thresholds over the groups to be equal was allowed, as indicated by the fit of the strong factorial invariance model (χ2 (36) = 43.66, p = 0.178; RMSEA = 0.017). Restricting the residual variances to be equal over the groups in the strict factorial invariance model was also permitted, based on the RMSEA (χ2 (71) = 119.21, p < 0.001; RMSEA = .031). This means that for different ages and sexes, the same proportion of the variance can be explained by the latent factor. The CAGE, as it is administered in our surveys, is thus measurement invariant over age and sex. Accordingly, answers on the CAGE can be compared from one age and sex to another. With the CAGE being measurement invariant over age and sex, differences in the prevalence are allowed for when these result from a difference at the latent factor level.
