Two-stage path analysis with definition variables: An alternative framework to account for measurement error

Area of Science:

• Psychological research methods
• Statistical modeling
• Structural equation modeling

Background:

• Structural equation modeling (SEM) is the gold standard for estimating path coefficients among psychological constructs with measurement error.
• Researchers often simplify models by using composite or factor scores, ignoring measurement error, especially with categorical indicators.
• Existing methods for continuous indicators do not address measurement error in categorical data.

Purpose of the Study:

• To introduce a general framework, two-stage path analysis (2S-PA) with definition variables, for path modeling with categorical indicators.
• To separate the estimation of factor scores and path coefficients, allowing for flexible model specification and easier assumption diagnostics.

Main Methods:

• Developed and applied the two-stage path analysis (2S-PA) framework.
• Conducted three simulation studies involving latent regression and mediation analysis with categorical indicators.
• Illustrated 2S-PA implementation using Mplus and OpenMx with a national dataset.

Main Results:

• 2S-PA produced similar estimates to SEM in large samples.
• 2S-PA demonstrated superior convergence rates, reduced standard error bias, and better Type I error control in small samples.
• The method effectively handles path modeling with categorical indicators.

Conclusions:

• 2S-PA provides a valuable alternative to SEM for path modeling with categorical indicators, particularly beneficial in small sample sizes.
• The separated estimation in 2S-PA enhances model flexibility and diagnostic capabilities.
• This framework offers practical implementation guidance for researchers.