The impact of measurement invariance and the provision for partial invariance in confirmatory factor analytic models on factor intercorrelations, latent mean differences, and estimates of relations with external variables is investigated for measures of two sets of widely assessed constructs: Big Five personality and the six Holland interests (RIASEC). In comparing models that include provisions for partial invariance with models that do not, the results indicate quite small differences in parameter estimates involving the relations between factors, one relatively large standardized mean difference in factors between the subgroups compared and relatively small differences in the regression coefficients when the factors are used to predict external variables. The results provide support for the use of partially invariant models, but there does not seem to be a great deal of difference between structural coefficients when the measurement model does or does not include separate estimates of subgroup parameters that differ across subgroups. Future research should include simulations in which the impact of various factors related to invariance is estimated. (Contains 6 tables and 1 figure.)