Beyond Moderation: Exploring Person-Level Mediation with Residuals and Individual Model Fit

Mediation analysis is integral to psychology, investigating human behavior’s causal mechanisms. The diversity of explanations for human behavior has implications for the estimation and interpretation of statistical mediation models. Individuals can have similar observed outcomes while undergoing different causal processes or different observed outcomes while receiving the same treatment. Researchers can employ diverse strategies when studying individual differences in multiple mediation pathways, including individual fit measures and analysis of residuals. This dissertation investigates the use of individual residuals and fit measures to identify individual differences in multiple mediation pathways. More specifically, this study focuses on mediation model residuals in a heterogeneous population in which some people experience indirect effects through one mediator and others experience indirect effects through a different mediator. A simulation study investigates 162 conditions defined by effect size and sample size for three proposed methods: residual differences, delta z, and generalized Cook’s distance. Results indicate that analogs of Type 1 error rates are generally acceptable for the method of residual differences, but statistical power is limited. Likewise, neither delta z nor gCd could reliably distinguish between contrasts that had true effects and those that did not. The outcomes of this study reveal the potential for statistical measures of individual mediation. However, limitations related to unequal subpopulation variances, multiple dependent variables, the inherent relationship between direct effects and unestimated indirect effects, and minimal contrast effects require more research to develop a simple method that researchers can use on single data sets.