Comparison of Frequentist and Bayesian Methods for Testing Measurement Invariance Between Groups

• Activity Number: 30
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Dmitriy Poznyak*
• Companies: Mathematica Policy Research
• Keywords: Measurement invariance ; Confirmatory Factor Analysis ; Exact and approximate equivalence ; Bayesian inference ; Latent Construct

Abstract

A key assumption of comparing latent constructs between groups is that the measurement properties of the instrument used to elicit these constructs is invariant. A lack of measurement invariance (MI) indicates that the groups interpret measures differently and simple comparisons of mean scores could confound the results. A common statistical method used for MI testing is multigroup confirmatory factor analysis estimated via frequentist inference (ML or WLS). This traditional approach implies that the variance-covariance structures between the groups are exactly equal. This restrictive assumption often hampers comparison of factor means across groups with different subject or cultural background. A recent Bayesian MI approach (Muthén and Asparouhov 2013) introduced the concept of approximate invariance where one can reasonably expect some differences across the groups. In the Bayesian MI approach, parameters (factor loadings or intercepts and slopes) are themselves considered variables with a specific distribution defined by empirical or non-empirical priors. Approximate MI allows for small differences (.01-.05 s.d.) between parameters otherwise constrained as equal in the exact app