SENSITIVITY ANALYSIS OF STRUCTURAL PARAMETERS TO MEASUREMENT NONINVARIANCE: A BAYESIAN APPROACH

Abstract

Most previous studies have argued that the validity of group comparisons of structural parameters is dependent on the extent to which measurement invariance is met. Although some researchers have supported the concept of partial invariance, there is still no clear-cut partial invariance level which is needed to make valid group comparisons. In addition, relatively little attention has been paid to the implications of failing measurement invariance (e.g., partial measurement invariance) on group comparison on the underlying latent constructs in the multiple-group confirmatory factor analysis (MGCFA) framework. Given this, the purpose of the current study was to examine the extent to which measurement noninvariance affects structural parameter comparisons across populations in the MGCFA framework. Particularly, this study takes a Bayesian approach to investigate the sensitivity of the posterior distribution of structural parameter difference to varying types and magnitudes of noninvariance across two populations. A Monte Carlo simulation was performed to empirically investigate the sensitivity of structural parameters to varying types and magnitudes of noninvariant measurement models across two populations from a Bayesian approach. In order to assess the sensitivity of noninvariance conditions, three outcome variables were evaluated: (1) accuracy of statistical conclusion on structural parameter difference, (2) precision of the estimated structural parameter difference, and (3) bias in the posterior mean of structural parameter difference. Inconsistent with findings of previous studies, the results of this study showed that the three outcome variables were not sensitive to varying types and magnitudes of noninvariance across all conditions. Instead, the three outcome variables were sensitive to sample size, factor loading size, and prior distribution. These results indicate that even under a large magnitude of measurement noninvariance, accurate conclusions and inferences on structural parameter differences across populations could be obtained in the MGCFA framework. Implications for practice are discussed for applied researchers who wish to conduct group comparisons of structural parameters across populations under measurement noninvariance.