Effect of Parameterization on Statistical Power and Effect Size Estimation in Latent Growth Modeling

Area of Science:

• Statistics
• Psychometrics
• Biostatistics

Background:

• Latent growth modeling (LGM) is commonly used to assess treatment efficacy by examining differences in random slopes between groups.
• End centering is a parameterization technique used in LGM with randomized designs.
• The interpretation of random intercepts and slopes differs based on the centering method employed.

Purpose of the Study:

• To investigate the statistical power and precision of detecting treatment effects using random intercepts versus random slopes in LGM with end centering.
• To provide recommendations for optimizing the analysis of treatment efficacy in randomized studies.

Main Methods:

• A Monte Carlo simulation study was conducted.
• Latent growth modeling with end centering was employed.
• Statistical power and standard errors for detecting treatment effects were compared between random intercept and random slope differences.

Main Results:

• Statistical power to detect treatment effects was significantly greater when assessed via the random intercept difference compared to the random slope difference.
• The standard error for the model-estimated mean difference was smaller when derived from the intercept difference, indicating greater precision.
• End centering facilitates the interpretation of the intercept difference as the mean difference at the study's end.

Conclusions:

• Investigators can reduce Type II errors by focusing on random intercept differences to test treatment effects in LGM with end centering.
• Power assessments for treatment effects should utilize end centering and focus on the intercept difference for enhanced detection.
• This approach improves the efficiency and accuracy of treatment efficacy evaluations in longitudinal studies.