Performance of location‑scale models in meta‑analysis: A simulation study

Abstract

Location-scale models in the field of meta-analysis allow researchers to simultaneously study the influence of moderator variables on the mean (location) and variance (scale) of the distribution of true effects. However, the increased complexity of such models can make model fitting challenging. Moreover, the statistical properties of the estimation and inference methods for such models have not been systematically examined in the meta-analytic context. We therefore conducted a Monte Carlo simulation study to compare different estimation methods (maximum or restricted maximum likelihood estimation), significance tests (Wald-type, permutation, and likelihood-ratio tests), and methods for constructing confidence intervals (Wald-type and profile-likelihood intervals) for the scale coefficients of such models. When restricted maximum likelihood estimation was used, slightly closer to nominal rejection rates and narrower confidence intervals were obtained. The permutation test yielded type I error rates closest to the nominal level, whereas the likelihood-ratio test obtained the highest statistical power. In most scenarios, profile-likelihood intervals showed lower coverage probabilities than the Wald-type method but closer to the nominal 95% level. Finally, slightly higher rejection rates and coverage probabilities were obtained when a dichotomous moderator was examined rather than a continuous one. Despite the need to use some constraints on the parameter space for the scale coefficients and the possibility of non-convergence of some procedures that may affect the fitting of the specified models, location-scale models proved to be a valid and useful tool for modeling the heterogeneity parameter in meta-analysis.