Multivariate Meta-Analysis of Vector Autoregressive Model Coefficients: A Two-Step Structural Equation Modeling Approach

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Abstract: 

This study introduces a novel approach to fitting discrete- and continuous-time multilevel vector autoregressive (VAR) models using meta-analysis from a structural equation modeling perspective. The methodology involves a two-stage process. In the first stage, VAR models are fitted to data from each individual, resulting in individual-specific coefficients and sampling variance-covariance matrices. In the second stage, these coefficients and matrices are synthesized using multivariate meta-analysis. Assuming the VAR estimates follow a multivariate normal distribution, we estimate the mean and covariance matrix to capture between-individual variability. By employing a structural equation modeling framework for meta-analysis, this approach allows for several extensions. For instance, it can include time-invariant covariates that affect within-individual estimates and incorporate the impact of VAR estimates on distal outcomes. Additionally, this method can consider a mixture of normal distributions instead of a single multivariate normal distribution, providing a more flexible representation of the data structure.