Abstract
Statistical mediation analysis is used to investigate mechanisms through which a randomized intervention causally affects an outcome variable. Mediation analysis is often carried out in a pretest-posttest control group design because it is a common choice for evaluating experimental manipulations in the behavioral and social sciences. There are four different two-wave (i.e., pretest-posttest) mediation models that can be estimated using either linear regression or a Latent Change Score (LCS) specification in Structural Equation Modeling: Analysis of Covariance, difference and residualized change scores, and a cross-sectional model. Linear regression modeling and the LCS specification of the two-wave mediation models provide identical mediated effect estimates but the two modeling approaches differ in their assumptions of model fit. Linear regression modeling assumes each of the four two-wave mediation models fit the data perfectly whereas the LCS specification allows researchers to evaluate the model constraints implied by the difference score, residualized change score, and cross-sectional models via model fit indices. Therefore, the purpose of this paper is to provide a conceptual and statistical comparison of two-wave mediation models. Models were compared on the assumptions they make about time-lags and cross-lagged effects as well as statistically using both standard measures of model fit (χ2, RMSEA, and CFI) and newly proposed T-size measures of model fit for the two-wave mediation models. Overall, the LCS specification makes clear the assumptions that are often implicitly made when fitting two-wave mediation models with regression. In a Monte Carlo simulation, the standard model fit indices and newly proposed T-size measures of model fit generally correctly identified the best fitting two-wave mediation model.
Highlights
The questions asked in analyses of randomized interventions are inherently about change
We tested the model constraints for the difference score, residualized change score, and cross-sectional models in our example and we found evidence that the non-ANCOVA models did not fit the data as well as the ANCOVA model the residualized change score model did not fit poorly
This paper extended previous work using the LCS specification to estimate two-wave mediation models by testing the performance of model fit statistics when evaluating which of the two-wave mediation models best describe the observed data
Summary
The questions asked in analyses of randomized interventions are inherently about change. The difference score, residualized change score, and cross-sectional models make very stringent assumptions about the relationship between the pretest and posttest measures for both the mediator and the outcome (Valente and MacKinnon, 2017). These assumptions are rarely evaluated, and we suspect that this lack of evaluation is because researchers did not have the tools or guidance to do so
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