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Bayesian (non)linear random effects mediation models: Evaluating the impact of omitting confounders
Ziwei Zhang1, Nidhi Kohli1, Eric F Lock2
1Department of Educational Psychology, University of Minnesota.
Researchers developed Bayesian nonlinear random effects mediation models (B(N)REMM) to directly estimate linear and nonlinear longitudinal mediation. Omitting confounders negatively impacts parameter recovery in these models, especially for segmented trends.
Area of Science:
- Psychometrics and Educational Measurement
- Statistical Modeling
- Longitudinal Data Analysis
Background:
- Longitudinal mediation models often rely on structural equation modeling, limiting the direct estimation of nonlinear functions.
- Existing methods require reparameterization to handle intrinsically nonlinear relationships in repeated measures data.
- The impact of omitting confounders in nonlinear longitudinal mediation has not been previously assessed.
Purpose of the Study:
- To develop a Bayesian framework, B(N)REMM, for directly modeling intrinsically linear and nonlinear longitudinal mediation.
- To introduce two specific models: linear (L-BREMM) and piecewise segmented (P-BREMM) longitudinal mediation models.
- To investigate the consequences of omitting confounders on model estimation and convergence.
Main Methods:
- Developed Bayesian (non)linear random effects mediation models (B(N)REMM) for longitudinal data.
- Implemented linear (L-BREMM) and piecewise linear (P-BREMM) models with unknown random changepoints.
- Utilized an empirical dataset (Early Childhood Longitudinal Study-Kindergarten Cohort) and Monte Carlo simulations to assess model performance and the impact of omitted confounders.
Main Results:
- The empirical example highlighted the necessity of including confounders to avoid model misspecification.
- Monte Carlo simulations demonstrated that omitting confounders negatively affects parameter recovery for both L-BREMM and P-BREMM.
- Omission of confounders impacted model convergence specifically for the P-BREMM model.
Conclusions:
- The B(N)REMM framework provides a direct approach for estimating linear and nonlinear longitudinal mediation.
- Model misspecification due to omitted confounders can lead to biased parameter estimates and convergence issues, particularly in segmented longitudinal models.
- The study provides R scripts for implementing L-BREMM and P-BREMM, facilitating broader application.
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