Regression-Equivalent Effect Sizes for Latent Growth Modeling and Associated Null Hypothesis Significance Tests

Area of Science:

• Psychometrics
• Statistical Modeling
• Longitudinal Data Analysis

Background:

• Traditional growth modeling with latent variables examines predictors of change using random slopes.
• This approach can be complex and may not always offer optimal statistical power.

Purpose of the Study:

• To demonstrate an alternative intercept-focused approach for analyzing the effect of covariates on growth.
• To show that this method yields equivalent effect sizes to classical regression analysis.
• To compare the statistical power of the intercept-focused approach versus the random slopes approach.

Main Methods:

• Utilizing final status centering for parameterization in latent growth models.
• Regressing random intercepts (or intercept factor scores) on an independent variable and a baseline covariate.
• Applying an intercept-focused framework analogous to classical regression analysis.

Main Results:

• The intercept-focused approach effectively estimates the same effect sizes (unstandardized regression coefficient, standardized regression coefficient, squared semi-partial correlation, Cohen's f² ) as classical regression.
• Statistical power for detecting predictor effects on growth was higher with the random intercepts method compared to the conventional random slopes method.

Conclusions:

• An intercept-focused approach provides a powerful and interpretable alternative for growth modeling.
• This method simplifies the analysis of predictors of change and enhances statistical power.
• Researchers can confidently apply this framework for more robust longitudinal data analysis.