Meta-analysis with standardized effect sizes from multilevel and latent growth models

Area of Science:

• Psychometrics
• Statistical Modeling
• Meta-Analysis

Background:

• Growth modeling analysis (GMA) findings are crucial for literature reviews.
• Existing methods for integrating GMA into meta-analysis are limited.
• Rarely discussed approaches are needed to improve the inclusion of GMA studies.

Purpose of the Study:

• To explicate four rarely discussed approaches for using GMA studies in meta-analysis.
• To present equations for calculating effect size (d) and its variance (v) from GMA studies.
• To demonstrate the application of these methods using a fixed effects meta-analysis.

Main Methods:

• Development of new and extant equations for calculating effect size (d) and variance (v) from GMA.
• Application of four distinct methods for integrating GMA into meta-analysis.
• Conducting a fixed effects meta-analysis of 5 randomized clinical trials.

Main Results:

• Common practices can bias effect sizes due to attrition, measurement errors, and assumption violations.
• A newer model-based framework and its GMA d statistic yield larger effect sizes.
• The proposed methods offer a more accurate estimation of treatment effects from GMA studies.

Conclusions:

• The optimal strategy involves using GMA d and its variance (v) calculated with the standard error of the unstandardized coefficient.
• When the standard error is unknown, GMA d and its v can be estimated using an alternative equation.
• These methods enhance the accurate inclusion of GMA studies in meta-analyses.