Robustness Conditions for MIIV-2SLS when the Latent Variable or Measurement Model is Structurally Misspecified

Bollen, Kenneth A.; Gates, Kathleen M.; & Fisher, Zachary. (2018). Robustness Conditions for MIIV-2SLS when the Latent Variable or Measurement Model is Structurally Misspecified. Structural Equation Modeling, 25(6), 848-59. PMCID: PMC6296771

Bollen, Kenneth A.; Gates, Kathleen M.; & Fisher, Zachary. (2018). Robustness Conditions for MIIV-2SLS when the Latent Variable or Measurement Model is Structurally Misspecified. Structural Equation Modeling, 25(6), 848-59. PMCID: PMC6296771

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Most researchers acknowledge that virtually all structural equation models (SEMs) are approximations due to violating distributional assumptions and structural misspecifications. There is a large literature on the unmet distributional assumptions, but much less on structural misspecifications. In this paper we examine the robustness to structural misspecification of the Model Implied Instrumental Variable, Two Stage Least Square (MIIV-2SLS) estimator of SEMs. We introduce two types of robustness: robust-unchanged and robust-consistent. We develop new robustness analytic conditions for MIIV-2SLS and illustrate these with hypothetical models, simulated data, and an empirical example. Our conditions enable a researcher to know whether, for example, a structural misspecification in the latent variable model influences the MIIV-2SLS estimator for measurement model equations and vice versa. Similarly, we establish robustness conditions for correlated errors. The new robustness conditions provide guidance on the types of structural misspecifications that affect parameter estimates and they assist in diagnosing the source of detected problems with MIIVs.




JOUR



Bollen, Kenneth A.
Gates, Kathleen M.
Fisher, Zachary



2018


Structural Equation Modeling

25

6

848-59








PMC6296771


11747

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