Causal Mediation Analysis with the Parallel Process Latent Growth Curve Mediation Model

Abstract

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and identification results for the interventional indirect effects via the mediator intercept (or slope) alone and due to their mutual dependence. For estimation, we proposed an interaction model that incorporates interactions among the mediator intercept/slope and treatment, coupled with a Bayesian method. We evaluated the studied methods through simulations, and illustrated their applications using an empirical example.

Keywords:

• Bayesian methods
• causal mediation analysis
• interventional indirect effects
• latent growth curve mediation models
• latent variable interactions

Acknowledegment

Lijuan Wang is grateful for the support from IES during the study.

Notes

1 The NDE and NIE presented in the main text have also been referred to as the “pure natural direct effect” and “total natural indirect effect”; alternatively, the total effect can be decomposed into the sum of the “total natural direct effect”, which is $E\left[Y(1,M(1))-Y(0,M(1))\right],$ and the “pure natural indirect effect”, which is $E\left[Y(0,M(1))-Y(0,M(0))\right]$ (Pearl, 2001; Robins & Greenland, 1992).

2 The term “identification” in causal inference refers to whether a causal estimand can be consistently estimated, which is a prerequisite for causal inference (Imai et al., 2010); the assumptions required for such identification are referred to as identification assumptions. To avoid potential confusion with the concept of identification in latent variable modeling (e.g., Bollen, 1989), we use “causal identification” (or “to causally identify”) to refer to the identification of (or to identify) causal estimands for causal inference in this article.

3 ${\text{IIE}}_{\mathit{\text{mu}}}^{\mathit{\text{IY}}}$ is also equal to the difference between the total effect of X on I_Y and the sum of ${\text{IDE}}^{\mathit{\text{IY}}}$ and the alternative versions of IIEs via I_M alone ($\text{alt}.{\text{IIE}}_{\mathit{\text{IM}}}^{\mathit{\text{IY}}}$) and via S_M alone ($\text{alt}.{\text{IIE}}_{\mathit{\text{SM}}}^{\mathit{\text{IY}}}$). That is, ${\text{TE}}^{\mathit{\text{IY}}}={\text{IDE}}^{\mathit{\text{IY}}}+{\text{IIE}}_{\mathit{\text{IM}}}^{\mathit{\text{IY}}}+{\text{IIE}}_{\mathit{\text{SM}}}^{\mathit{\text{IY}}}+{\text{IIE}}_{\mathit{\text{mu}}}^{\mathit{\text{IY}}},$ or ${\text{TE}}^{\mathit{\text{IY}}}={\text{IDE}}^{\mathit{\text{IY}}}+\text{alt}.{\text{IIE}}_{\mathit{\text{IM}}}^{\mathit{\text{IY}}}+\text{alt}.{\text{IIE}}_{\mathit{\text{SM}}}^{\mathit{\text{IY}}}+\text{alt}.{\text{IIE}}_{\mathit{\text{mu}}}^{\mathit{\text{IY}}}.$

4 The GCR (Hertzog et al., 2008; McArdle & Epstein, 1987) of the manifest mediator at the second time point is calculated by $\frac{{\sigma }_{I_M}^2}{{\sigma }_{I_M}^2+{\sigma }_{\mathit{\text{eM}}}^2},$ as the mediator slope loading at the second time point is 0. Similarly, the GCR of the manifest outcome at the last time point is calculated by $\frac{{\sigma }_{I_Y}^2}{{\sigma }_{I_Y}^2+{\sigma }_{\mathit{\text{eY}}}^2},$ because the outcome slope loading at the last time point is 0.

5 $\mathit{\text{GRR}}=\frac{{\sigma }_S^2}{{\sigma }_S^2+\frac{{\sigma }_e^2}{\mathit{\text{SST}}}},$ with $\mathit{\text{SST}}={\sum }_{t=1}^T{({\mathit{\text{Time}}}_t-\overline{\mathit{\text{Time}}})}^2,{\sigma }_S^2$ being the slope variance, and ${\sigma }_e^2$ being the within-person residual variance (Rast & Hofer, 2014; Willett, 1989).

Additional information

Funding

This work was supported by the Institute of Education Sciences IES grant R305D210023.