arXiv subjects

Kenneth A. Bollen

Publications and source records attributed to Kenneth A. Bollen.

3 recordsLinked to original sources

arXiv2024

Optimal Instrument Selection using Bayesian Model Averaging for Model Implied Instrumental Variable Two Stage Least Squares Estimators

Model-Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) is a limited information, equation-by-equation, non-iterative estimator for latent variable models. Associated with this estimator are equation specific tests of model misspecification. One issue with equation specific tests is that they lack specificity, in that they indicate that some instruments are problematic without revealing which specific ones. Instruments that are poor predictors of their target variables (weak instruments) is a second potential problem. We propose a novel extension to detect instrument specific tests of misspecification and weak instruments. We term this the Model-Implied Instrumental Variable Two-Stage Bayesian Model Averaging (MIIV-2SBMA) estimator. We evaluate the performance of MIIV-2SBMA against MIIV-2SLS in a simulation study and show that it has comparable performance in terms of parameter estimation. Additionally, our instrument specific overidentification tests developed within the MIIV-2SBMA framework show increased power to detect specific problematic and weak instruments. Finally, we demonstrate MIIV-2SBMA using an empirical example.

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arXiv2023

Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models

Measurement error is ubiquitous in many variables - from blood pressure recordings in physiology to intelligence measures in psychology. Structural equation models (SEMs) account for the process of measurement by explicitly distinguishing between latent variables and their measurement indicators. Users often fit entire SEMs to data, but this can fail if some model parameters are not identified. The model-implied instrumental variables (MIIVs) approach is a more flexible alternative that can estimate subsets of model parameters in identified equations. Numerous methods to identify individual parameters also exist in the field of graphical models (such as DAGs), but many of these do not account for measurement effects. Here, we take the concept of "latent-to-observed" (L2O) transformation from the MIIV approach and develop an equivalent graphical L2O transformation that allows applying existing graphical criteria to latent parameters in SEMs. We combine L2O transformation with graphical instrumental variable criteria to obtain an efficient algorithm for non-iterative parameter identification in SEMs with latent variables. We prove that this graphical L2O transformation with the instrumental set criterion is equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can lead to novel identification strategies when combined with other graphical criteria.

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arXiv2019

An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations

Methodological development of the Model-implied Instrumental Variable (MIIV) estimation framework has proved fruitful over the last three decades. Major milestones include Bollen's (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 \& Maydeu-Olivares, 2007), and the introduction of a Generalized Method of Moments (GMM) estimator (Bollen, Kolenikov \& Bauldry, 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.

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