An introduction to model implied instrumental variables using two stage least squares (MIIV-2SLS) in structural...

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Structural Equation Models (SEMs) are prevalent for analyzing complex systems with latent variables and measurement error.
• Maximum Likelihood (ML) and Diagonally Weighted Least Squares (DWLS) are standard SEM estimation techniques but can falter with model misspecifications or nonconvergence.
• Alternative robust methods are needed to address limitations of traditional SEM estimation.

Purpose of the Study:

• To provide a comprehensive overview and tutorial of the Model Implied Instrumental Variable, Two Stage Least Squares (MIIV-2SLS) method.
• To demonstrate the robustness of MIIV-2SLS to structural misspecifications and its noniterative nature.
• To guide researchers in applying MIIV-2SLS through a step-by-step process with an empirical example.

Main Methods:

• Detailed explanation of the six key steps for applying MIIV-2SLS: model specification, identification, latent to observed variable transformation, finding MIIVs, 2SLS estimation, and tests of overidentified equations.
• Illustration of each step using a running empirical example from a helping behavior experiment.
• Discussion of analytical conditions for robustness to structural misspecifications.

Main Results:

• MIIV-2SLS provides a noniterative and robust estimation approach for SEMs, outperforming ML and DWLS when models are misspecified.
• The tutorial effectively demonstrates the practical application of MIIV-2SLS across various statistical modeling scenarios.
• The method is shown to be effective in handling complex data structures and potential estimation challenges.

Conclusions:

• MIIV-2SLS is a powerful and versatile technique for estimating SEMs, particularly when robustness to misspecification and avoidance of convergence issues are critical.
• The article serves as a valuable resource for researchers seeking to implement advanced SEM techniques.
• Extensions for covariance matrices, multilevel SEM, categorical data, and causal inference highlight the broad applicability of MIIV-2SLS.