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

Abstract

The effect of an independent variable on random slopes in growth modeling with latent variables is conventionally used to examine predictors of change over the course of a study. This article demonstrates that the same effect of a covariate on growth can be obtained by using final status centering for parameterization and regressing the random intercepts (or the intercept factor scores) on both the independent variable and a baseline covariate–the framework used to study change with classical regression analysis. Examples are provided that illustrate the application of an intercept-focused approach to obtain effect sizes–the unstandardized regression coefficient, the standardized regression coefficient, squared semi-partial correlation, and Cohen’s f²–that estimate the same parameters as respective effect sizes from a classical regression analysis. Moreover, statistical power to detect the effect of the predictor on growth was greater when using random intercepts than the conventionally used random slopes.

Keywords:

• Effect sizes
• latent growth models
• multilevel analysis
• regression
• statistical power

Acknowledgements

I would like to thank Mike Stoolmiller for writing the R program that generates parameters for effect sizes used in the Monte Carlo study and for assistance with the Mplus programming for the illustrative and Monte Carlo analyses.

Additional information

Funding

This work was supported by National Institutes of Health (NIH)/National Institute on Alcohol Abuse and Alcoholism (NIAAA) grant R01AA025069. The content is solely the responsibility of the author and does not necessarily represent the official views of the NIH or NIAAA.