Citation
Bollen, Kenneth A.; Fisher, Zachary F.; Giordano, Michael L.; Lilly, Adam G.; Luo, Lan; & Ye, Ai (2022). An Introduction to Model Implied Instrumental Variables Using Two Stage Least Squares (MIIV-2SLS) in Structural Equation Models (SEMs). Psychological Methods, 27(5), 752-772. PMCID: PMC8799757Abstract
Structural equation models (SEMs) are widely used to handle multiequation systems that involve latent variables, multiple indicators, and measurement error. Maximum likelihood (ML) and Diagonally Weighted Least Squares (DWLS) dominate the estimation of SEMs with continuous or categorical endogenous variables, respectively. When a model is correctly specified, ML and DWLS function well. But, in the face of incorrect structures or nonconvergence, their performance can seriously deteriorate. Model Implied Instrumental Variable, Two Stage Least Squares (MIIV-2SLS) estimates and tests individual equations, is more robust to misspecifications, and is noniterative, thus avoiding nonconvergence. This paper is an overview and tutorial on MIIV-2SLS. It reviews the six major steps in using MIIV-2SLS: 1) model specification, 2) model identification, 3) latent to observed (L2O) variable transformation, 4) finding MIIVs, 5) using 2SLS, and 6) tests of overidentified equations. Each step is illustrated using a running empirical example from Reisenzein’s (1986) randomized experiment on helping behavior. We also explain and illustrate the analytic conditions under which an equation estimated with MIIV-2SLS is robust to structural misspecifications. We include additional sections on MIIV approaches using a covariance matrix and mean vector as data input, conducting multilevel SEM, analyzing categorical endogenous variables, causal inference, and extensions and applications. Supplemental online material illustrates input code for all examples and simulations using the R package MIIVsem.URL
http://dx.doi.org/10.1037/met0000297Reference Type
Journal ArticleYear Published
2022Journal Title
Psychological MethodsAuthor(s)
Bollen, Kenneth A.Fisher, Zachary F.
Giordano, Michael L.
Lilly, Adam G.
Luo, Lan
Ye, Ai
Article Type
RegularPMCID
PMC8799757Continent/Country
NonspecificORCiD
Bollen - 0000-0002-6710-3800Lilly - 0000-0002-3740-1540
Fisher, Z. - 0000-0003-2744-5141