Robustness Conditions for MIIV-2SLS When the Latent Variable or Measurement Model is Structurally Misspecified. Issue 6 (2nd November 2018)

• Record Type: Journal Article
• Authors: Bollen, Kenneth A.; Gates, Kathleen M.; Fisher, Zachary
• Is Part Of: Structural equation modeling. Volume 25:Issue 6(2018)
• Page Start: 848
• Page End: 859
• Publication Date: 2018-11-02
• Subjects: 2SLS -- MIIV -- model implied instrumental variables -- robustness -- structural misspecifications; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2018.1456341
• Languages: English
• ISSNs: 1070-5511

Abstract

Abstract : 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.