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.
Highlights
Structural equation modeling (SEM) is widely used in social and behavior sciences
Since the model-implied instrumental variable (MIIV) approach uses the scaling indicators to set the scale of η, we explore two choices of the scaling indicator, i.e., the indicators with standardized factor loadings 0.8 and the indicators with standardized factor loadings 0.5
We proposed a unified MIIV approach that handles a mixture of continuous, ordinal, or binary observed endogenous variables in SEM
Summary
Structural equation modeling (SEM) is widely used in social and behavior sciences. Endogenous observed variables (e.g., indicators) in a SEM model can be continuous, binary, ordinal, or censored. When binary or ordinal observed endogenous variables are present, researchers frequently use unweighted least squares (ULS, Muthén, 1978) and diagonally weighted least squares (DWLS, Muthén et al, 1997). These estimators require the estimation of a polychoric correlation matrix as a first stage. They use the polychoric correlation matrix as input and apply systemwide estimators such as ML, ULS, and DWLS. They are systemwide in the sense that all parameter estimates for all equations in the whole structural equation model are estimated simultaneously.
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