Citation
Bollen, Kenneth A.; Kolenikov, Stanislav; & Bauldry, Shawn (2014). Model-Implied Instrumental Variable – Generalized Method of Moments (MIIV–GMM) Estimators for Latent Variable Models. Psychometrika, 79(1), 20-50. PMCID: PMC6705389Abstract
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.URL
http://dx.doi.org/10.1007/S11336-013-9335-3Reference Type
Journal ArticleYear Published
2014Journal Title
PsychometrikaAuthor(s)
Bollen, Kenneth A.Kolenikov, Stanislav
Bauldry, Shawn
PMCID
PMC6705389ORCiD
Bollen - 0000-0002-6710-3800Bauldry - 0000-0002-6679-3125