Can we include dichotomous variables in meta-analytic structural equation modeling? Mind the prevalence.

Area of Science:

• Psychometrics
• Biostatistics
• Quantitative Psychology

Background:

• Meta-analytic structural equation modeling (MASEM) synthesizes study results by pooling correlations.
• Incorporating dichotomous variables into MASEM is challenging due to data input requirements.
• Standardized mean differences (e.g., Cohen's d) from primary studies need conversion to correlation matrices for MASEM.

Purpose of the Study:

• To investigate suitable conversion formulas for standardized mean differences to point-biserial correlations for MASEM.
• To examine the impact of prevalence, sampling plans, and group distribution on these conversions.
• To provide guidance for meta-analysts when including dichotomous variables in MASEM.

Main Methods:

• Three Monte Carlo simulation studies were conducted.
• Simulations varied prevalence, sampling plans, within-study sample sizes, and group distributions.
• The suitability of different conversion formulas was assessed under these conditions.

Main Results:

• The choice of conversion formula depends on the meta-analyst's specific objectives.
• When sample group distribution deviates from population prevalence, adjustments to correlations are necessary.
• Existing challenges in MASEM with dichotomous variables can be addressed with appropriate conversions and adjustments.

Conclusions:

• MASEM can effectively incorporate dichotomous variables with appropriate conversion of effect sizes.
• Meta-analysts must consider the distribution of dichotomous variables for accurate model fitting.
• An extended web application is available to assist with these conversions and adjustments.