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A Unified Model-Implied Instrumental Variable Approach for Structural Equation Modeling with Mixed Variables – Carolina Center for Population Aging and Health

A Unified Model-Implied Instrumental Variable Approach for Structural Equation Modeling with Mixed Variables

Citation

Jin, Shaobo; Yang-Wallentin, Fan; & Bollen, Kenneth A. (2021). A Unified Model-Implied Instrumental Variable Approach for Structural Equation Modeling with Mixed Variables. Psychometrika, 86(2), 564-594.

Abstract

The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal . We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.

URL

http://dx.doi.org/10.1007/s11336-021-09771-4

Reference Type

Journal Article

Article Type

Regular

Year Published

2021

Journal Title

Psychometrika

Author(s)

Jin, Shaobo
Yang-Wallentin, Fan
Bollen, Kenneth A.