34. SPSS AMOS How to test Measurement Model Invariance - Configural Invariance and Metric Invariance

Measurement model invariance testing is used to verify that survey indicators measure the same underlying construct across different groups (such as male vs. female, or customers from different cities/countries) or across different data-collection methods. In practice, it answers a practical reviewer concern: do the factor structure and indicator meanings stay stable when group membership changes? When invariance fails, the unobservable construct can shift—meaning respondents may interpret the same items differently across groups, undermining any comparison of latent variables.

The transcript focuses on two core levels of invariance that are commonly required: configural invariance and metric invariance. Configural invariance checks whether the overall factor structure fits similarly in each group—essentially, whether the same number of factors and the same pattern of factor-indicator relationships can represent the data for both groups. In AMOS, this is tested by running an unconstrained multi-group CFA (no equality constraints across groups) and then evaluating model fit indices such as CFI, TLI, and RMSEA. If the unconstrained model shows acceptable fit for both groups, the factor structure is treated as equivalent at the configural level.

After establishing configural invariance, metric invariance tests whether indicator factor loadings are equivalent across groups. This step targets the “basic meaning” of the construct: if loadings differ, the indicators do not contribute to the latent variable in the same way across groups. In AMOS, metric invariance is implemented by constraining factor loadings to be equal across groups and then comparing this constrained model to the earlier unconstrained model. The key decision rule is based on the chi-square difference: the constrained model should not produce a statistically significant deterioration in fit. The transcript emphasizes that non-significant chi-square differences indicate metric invariance—meaning indicator meanings remain consistent across groups.

The workflow described is operational and step-by-step. First, groups are defined in AMOS by selecting a grouping variable (e.g., gender) and assigning values to each group (e.g., male = 1, female = 2). Next, parameters must be labeled for each group so AMOS can apply constraints correctly; the transcript notes that AMOS can automatically name parameters via the multiple-group analysis setup, avoiding manual labeling even when models include many indicators. Once groups are defined and the unconstrained model is run, the analysis proceeds to the constrained metric invariance model and then uses model comparison output to check whether the chi-square change is significant.

Finally, the transcript outlines additional invariance tests that extend beyond metric invariance—often used when deeper equivalence is needed. These include scalar invariance (constraining factor loadings and measurement intercepts), factor variance invariance (constraining factor covariances/variances, sometimes framed as structural invariance), and error variance invariance (constraining residuals). Across all these stages, the guiding logic remains the same: compare constrained models to the unconstrained baseline and look for non-significant chi-square differences, signaling that added constraints do not harm model fit and that comparisons across groups are defensible.