Effect size measure for mediation analysis with a multicategorical predictor

Many currently available effect size measures for mediation have limitations when the predictor is nominal with three or more categories. The mediation effect size measure υ was adopted for this situation. A simulation study was conducted to investigate the performance of its estimators. We manipulated several factors in data generation (number of groups, sample size per group, and effect sizes of paths) and effect size estimation [different R-squared (R(2)) shrinkage estimators]. Results showed that the Olkin–Pratt extended adjusted R(2) estimator had the least bias and the smallest MSE in estimating υ across conditions. We also applied different estimators of υ in a real data example. Recommendations and guidelines were provided about the use of this estimator.