Estimation of Non-Directed Parameters in MIIV Structural Equation Modeling

Model-implied instrumental variable (MIIV) estimation provides a limited-information alternative to maximum likelihood estimation in structural equation modeling. MIIV estimation proceeds in two stages: directed parameters are estimated first, followed by the remaining variance and covariance parameters. We revisit this second stage from a weighted least squares perspective, showing that it comprises a family of estimators that includes unweighted least squares, generalized least squares, two-step reweighted least squares, and fully iterated reweighted least squares. All but the fully iterated reweighted least squares estimator have closed-form solutions. We also establish the relationship between model-based and unrestricted standard errors for the directed parameters. An exploratory simulation study illustrates the promising finite-sample behavior of these estimators. All estimators are implemented in the R package lavaan.