Maximum Likelihood Analysis of Linear Mediation Models with Treatment-Mediator Interaction

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Mediation models are widely used to understand indirect effects.
• Existing methods like IFGLS may provide inconsistent variance estimates for mediation models with correlated residuals.
• The current mediation model structure is not a system of seemingly unrelated regressions (SURs).

Purpose of the Study:

• To develop and present a Full-Information Maximum Likelihood Estimation (FIMLE) method for linear mediation models with correlated residuals.
• To derive consistent variance matrix estimates for the FIMLE method.
• To compare the theoretical properties of FIMLE with the iterative feasible generalized least squares (IFGLS) method.

Main Methods:

• Development of a linear mediation model with a treatment-mediator interaction term and correlated residuals.
• Application of Full-Information Maximum Likelihood Estimation (FIMLE) under normality assumptions.
• Derivation of a consistent variance matrix for FIMLE estimates.
• Theoretical comparison between FIMLE and IFGLS variance matrices.

Main Results:

• Parameters in the specified mediation model are partially identifiable under random assignment.
• FIMLE provides explicit estimates and a consistent variance matrix for model parameters.
• IFGLS estimates are consistent, but their variance matrix is not consistent for this model.
• Theoretical analysis and simulation studies support the superiority of FIMLE's variance estimation.

Conclusions:

• The FIMLE method offers a statistically sound approach for estimating mediation models with correlated residuals.
• The developed FIMLE method provides more accurate variance estimation compared to IFGLS.
• The FIMLE method has been implemented in the R package iMediate for practical application.