Limited Information Parameter Estimates for Latent or Mixed Manifest and Latent Variable Models

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Latent variable models are widely used but often analyzed using full information techniques.
• Separate analysis of measurement and structural components can offer distinct advantages.
• Existing methods may not optimally detect specific types of model misspecifications.

Purpose of the Study:

• To propose and evaluate limited information (single equation) procedures for parameter estimation in the structural part of latent variable models.
• To compare the performance of limited versus full information estimates in detecting structural model misspecifications.
• To provide recommendations for choosing between estimation techniques for causal hypothesis testing and model diagnostics.

Main Methods:

• Development of limited information parameter estimation procedures for recursive and nonrecursive structural models.
• Implementation of procedures for testing zero-effect hypotheses within these models.
• Monte Carlo simulation comparing full and limited information estimates using misspecified structural models.

Main Results:

• Both full and limited information estimates effectively identified misspecified nonzero effects.
• Limited information estimates demonstrated superior performance in detecting misspecified zero-effect hypotheses.
• The study highlights the utility of limited information methods for specific hypothesis testing and misspecification detection.

Conclusions:

• Separate analysis of structural models using limited information procedures is recommended.
• Limited information techniques are particularly advantageous for testing specific causal hypotheses.
• These methods are highly effective for locating specific structural model misspecifications, especially zero-effect hypotheses.