R-squared change in structural equation models with latent variables and missing data.

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Assessing incremental validity is crucial for establishing the unique contribution of a construct.
• Traditional OLS regression's R-squared (R²) is straightforward, but SEMs with latent variables present challenges for ΔR² calculation.
• Measurement error in observed variables can lead to biased estimates and inflated Type I error rates, necessitating latent variable modeling.

Purpose of the Study:

• To describe and compare four novel approaches for calculating the change in R-squared (ΔR²) in structural equation models (SEMs) with latent variables.
• To address the complexities of ΔR² calculation in SEMs, particularly when dealing with missing data.
• To provide practical tools (R functions) for researchers to implement these methods.

Main Methods:

• The study proposes four distinct methods for computing ΔR² in SEMs with latent variables.
• Performance of these methods was evaluated through simulation studies.
• Extensions to the methods were explored, and R functions were developed for practical application.

Main Results:

• The simulation results indicate the comparative performance of the four proposed ΔR² calculation approaches.
• The developed R functions facilitate the implementation of these methods in SEM analyses.
• The study addresses the impact of missing data on ΔR² estimation in SEMs.

Conclusions:

• Accurate calculation of ΔR² in SEMs with latent variables is now feasible using the presented methods.
• These approaches enhance the ability of researchers to make robust incremental validity claims.
• The provided R functions offer practical solutions for researchers employing SEM and seeking to quantify effect sizes.