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Model-Implied Instrumental Variable—Generalized Method of Moments (MIIV-GMM) Estimators for Latent Variable Models

Author

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  • Kenneth Bollen

  • Stanislav Kolenikov

  • Shawn Bauldry

Abstract

The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes model-implied instrumental variable – generalized method of moments (MIIV-GMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions, the MIIV-GMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are “distribution-free,” robust to heteroscedasticity, and have overidentification goodness-of-fit J-tests with asymptotic chi-square distributions. In addition, MIIV-GMM estimators are “scalable” in that they can estimate and test the full model or any subset of equations, and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIV-GMM estimators. Two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes. Copyright The Psychometric Society 2014

Suggested Citation

  • Kenneth Bollen & Stanislav Kolenikov & Shawn Bauldry, 2014. "Model-Implied Instrumental Variable—Generalized Method of Moments (MIIV-GMM) Estimators for Latent Variable Models," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 20-50, January.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:20-50
    DOI: 10.1007/s11336-013-9335-3
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    References listed on IDEAS

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    1. Steven Andrew Culpepper & Herman Aguinis & Justin L. Kern & Roger Millsap, 2019. "High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 285-309, March.
    2. Kenneth A. Bollen & Kathleen M. Gates & Lan Luo, 2024. "A Model Implied Instrumental Variable Approach to Exploratory Factor Analysis (MIIV-EFA)," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 687-716, June.
    3. Hayakawa, Kazuhiko, 2019. "Alternative over-identifying restriction test in the GMM estimation of panel data models," Econometrics and Statistics, Elsevier, vol. 10(C), pages 71-95.
    4. Christian Gische & Manuel C. Voelkle, 2022. "Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 868-901, September.
    5. Viviana Amati & Felix Schönenberger & Tom A. B. Snijders, 2019. "Contemporaneous Statistics for Estimation in Stochastic Actor-Oriented Co-evolution Models," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1068-1096, December.
    6. Liu, Steven Y.H. & Deligonul, Seyda & Cavusgil, S. Tamer & Chiou, Jyh-Shen, 2021. "Addressing psychic distance and learning in international buyer-seller relationships: The role of firm exploration and asset specificity," Journal of World Business, Elsevier, vol. 56(4).
    7. Shaobo Jin & Fan Yang-Wallentin & Kenneth A. Bollen, 2021. "A unified model-implied instrumental variable approach for structural equation modeling with mixed variables," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 564-594, June.
    8. Zachary F. Fisher & Kenneth A. Bollen, 2020. "An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 660-683, September.

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