Longitudinal Measurement Invariance in a Two-Wave Mediation Model

Introduction: Statistical mediation analysis is commonly used in prevention research to evaluate interventions. A critical assumption of the mediation model is the temporal precedence of the mediator before outcome. Temporal precedence can be modeled explicitly in longitudinal mediation designs (Cole & Maxwell, 2003; MacKinnon, 1994) where pre-test information on the mediator and outcome is included in the estimation of the mediated effect (Valente & MacKinnon, 2016). However, when data on the mediator and outcome are collected at multiple time points, it is assumed that researchers are measuring the same construct at each measurement occasion (Widaman, Ferrer, & Conger, 2010). In other words, the mediator and outcome at pre- and post-test are assumed to be measurement invariant, defined as having the same factor structure across time (same factor loadings, intercepts, and residual variances), in order to make accurate inference of change. Although the hypothesis of longitudinal measurement invariance can be tested under the confirmatory factor analysis framework (Meredith, 1993), the consequences of violating longitudinal measurement invariance on mediated effect estimation have not been extensively investigated (Olivera-Aguilar et al., 2016). The purpose of the poster presentation is to demonstrate how to test for longitudinal measurement invariance in the two-wave mediation model and to investigate how violating longitudinal measurement invariance can influence the estimation of the mediated effect in the two-wave model.

Method: Monte Carlo simulation methods were used to investigate the properties of mediated effect estimation in the two-wave, longitudinal mediation model when there were violations of longitudinal measurement invariance in both the mediator and the outcome, respectively. Study conditions included varying effect size of the mediated effect and magnitudes of factor loadings and factor intercept noninvariance across time for the mediator and outcome constructs using an approach outlined by Yoon and Millsap (2007) and Millsap & Olivera-Aguilar (2012).

Results: Results suggested that the estimation of the mediated effect was robust to violations of measurement invariance in the factor loadings of the constructs, but that the mediated effect was biased in the presence of non-invariance in the factor intercepts. Implications on power and confidence interval coverage of the mediated effect are also discussed.

Conclusions: Results suggest the importance of evaluating longitudinal measurement invariance for accurate estimation of the mediated effect in two-wave designs. This poster raises awareness of the importance of psychometric and measurement theory in the statistical mediation model.