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

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

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)848-859
Number of pages12
JournalStructural Equation Modeling
Issue number6
StatePublished - Nov 2 2018

All Science Journal Classification (ASJC) codes

  • General Decision Sciences
  • Modeling and Simulation
  • Sociology and Political Science
  • Economics, Econometrics and Finance(all)


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