Markov chain Monte Carlo Estimation Methods for Structural Equation Modeling: A Comparison of Subject-level Data and Moment-level Data Approaches

Structural equation modeling [1] has been used in a variety of research applications in the social and behavioral sciences. A broad-spectrum aim of SEM can be expressed as testing the hypothesis that the population-level covariance matrix for a set of measured indicator variables is equal to the model-implied covariance matrix based on the hypothesized factor model. And, this relationship can be expressed as Σ = Σ(θ) where Σ represents the population covariance matrix of a set of observed indicator variables and Σ(θ) represents the model implied covariance matrix as a function of θ, a vector of model parameters.