Department of statistics, Uppsala University, Uppsala, Sweden.
Department of psychology and neuroscience, Department of sociology, University of North Carolina at Chapel Hill, Chapel Hill, USA.
Psychometrika. 2021 Jun;86(2):564-594. doi: 10.1007/s11336-021-09771-4. Epub 2021 Jun 7.
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.
模型隐含工具变量（MIIV）估计器是结构方程模型的逐方程估计器，比完全信息估计器更能抵抗结构误设。先前的研究集中于全部是连续的（MIIV-2SLS）或全部是有序的内生变量。我们开发了一种统一的 MIIV 方法，适用于混合的二项式、有序、删失或连续的内生观测变量。我们包括因子载荷、回归系数、方差和协方差的估计值及其渐近标准误差。此外，我们还创建了模型拟合优度的新检验和单方程过度识别检验。我们的模拟研究表明，与对角线加权最小二乘法（DWLS）相比，所提出的 MIIV 方法对结构误设更具稳健性，而且拟合优度模型检验和过度识别方程检验都可以检测到结构误设。我们还发现，因子载荷和回归系数的 MIIV 估计量的渐近标准误差的偏差通常低于 DWLS 的，尽管在大样本中差异很小。我们的分析表明，可靠性低的指标会对 MIIV 估计量产生不利影响。此外，使用 MIIV 的一小部分子集可以减少系数估计的小样本偏差，但会降低方程过度识别检验的功效。
