An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations
- PDF / 522,919 Bytes
- 24 Pages / 547.087 x 737.008 pts Page_size
- 78 Downloads / 154 Views
AN INSTRUMENTAL VARIABLE ESTIMATOR FOR MIXED INDICATORS: ANALYTIC DERIVATIVES AND ALTERNATIVE PARAMETERIZATIONS
Zachary F. Fisher UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
Kenneth A. Bollen UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
Methodological development of the model-implied instrumental variable (MIIV) estimation framework has proved fruitful over the last three decades. Major milestones include Bollen’s (Psychometrika 61(1):109–121, 1996) original development of the MIIV estimator and its robustness properties for continuous endogenous variable SEMs, the extension of the MIIV estimator to ordered categorical endogenous variables (Bollen and Maydeu-Olivares in Psychometrika 72(3):309, 2007), and the introduction of a generalized method of moments estimator (Bollen et al., in Psychometrika 79(1):20–50, 2014). This paper furthers these developments by making several unique contributions not present in the prior literature: (1) we use matrix calculus to derive the analytic derivatives of the PIV estimator, (2) we extend the PIV estimator to apply to any mixture of binary, ordinal, and continuous variables, (3) we generalize the PIV model to include intercepts and means, (4) we devise a method to input known threshold values for ordinal observed variables, and (5) we enable a general parameterization that permits the estimation of means, variances, and covariances of the underlying variables to use as input into a SEM analysis with PIV. An empirical example illustrates a mixture of continuous variables and ordinal variables with fixed thresholds. We also include a simulation study to compare the performance of this novel estimator to WLSMV. Key words: estimation, latent variables, ordinal variables, dichotomous variables, continuous variables, instrumental variables, two-stage least squares (2SLS), factor analysis, structural equation modeling.
1. Introduction Classic structural equation models (SEMs) treated all endogenous variables as continuous. Contemporary SEM research has paid more attention to binary, ordinal, and other noncontinuous endogenous variables (Arminger and Küsters 1988; Muthén 1984; 1993; Jöreskog 1994). Item response theory (IRT), of course, has a long history of treating measurement models with binary or ordinal measures (e.g. Thurstone 1925; Lazarsfeld 1950; Bock 1972; Lord et al. 1968). A number of estimators have also been proposed for SEMs with categorical endogenous variables, including the diagonally weighted least squares (DWLS), full-information maximum likelihood (FIML), pairwise maximum likelihood (Katsikatsou et al. 2012, PML), and polychoric instrumental variable (Bollen and Maydeu-Olivares 2007, PIV) estimators. Recent research on the PIV estimator has revealed some promising features. Nestler (2013) found the PIV estimator to be as accurate as the unweighted least squares (ULS) and DWLS estimators for correctly specified models and more robust in the presence of structural misspecifications. Similarly, Jin et al. (2016) found the PIV estimates to be as good as those from
Data Loading...
