Teacher's Corner: Testing Measurement Invariance of Second-Order Factor Models

TLDR

The study demonstrates how to test measurement invariance in a second‑order factor model using a quality‑of‑life dataset of 924 participants. The authors tested invariance across seven hierarchical levels—configural, first‑ and second‑order loadings, intercepts of variables and factors, disturbances, and residuals—using confirmatory factor analysis in LISREL 8.51 on the mean and covariance structures. Measurement invariance was confirmed at loading and intercept levels, allowing estimation of a latent mean difference on the higher‑order factor, and the study discusses the implications for psychological research using second‑order factor models.

Abstract

We illustrate testing measurement invariance in a second-order factor model using a quality of life dataset (n = 924). Measurement invariance was tested across 2 groups at a set of hierarchically structured levels: (a) configural invariance, (b) first-order factor loadings, (c) second-order factor loadings, (d) intercepts of measured variables, (e) intercepts of first-order factors, (f) disturbances of first-order factors, and (g) residual variances of observed variables. Given that measurement invariance at the factor loading and intercept levels was achieved, the latent factor mean difference on the higher order factor between the groups was also estimated. The analyses were performed on the mean and covariance structures within the framework of the confirmatory factor analysis using the LISREL 8.51 program. Implications of second-order factor models and measurement invariance in psychological research were discussed.