Structural Equation Modeling with Time Series Data

Abstract

Structural Equation Modeling (SEM), also commonly referred to as path analysis in the absence of latent variables, is a powerful multivariate analysis approach to explore and to confirm causal relationships. It imposes a structure on the covariance matrix and the imposed structure is subsequently validated by the data. In recent years, SEM has been extended to analyze autoregressive moving average (ARMA) time series data assuming time-constant path coefficients. The mechanism of ARMA-based SEM makes it the ideal procedure for the analysis of directional brain functional pathways based on the multi-subject, multivariate time series data generated through the functional magnetic resonance imaging (fMRI) studies. However the time-constant path coefficient assumption is unrealistic and overly restrictive. In this work, based on converting the overall SEM to the sectional SEM approach for vector ARMA(p, q) time series, we extend the ARMA-based SEM to allow time-varying coefficients (TVC). The statistical inference framework based on the maximum likelihood method is derived and the advantage of the novel TVC SEM approach is demonstrated through simulation studies. In addition, we also applied the new method to examine the brain visual-attention pathway based on an fMRI experiment conducted at the Brookhaven National Laboratory. Other than brain functional pathways studies, the TVC SEM method can be readily applied to analyze other longitudinal data such as the financial time series.