Computationally efficient interval estimation for the 1-1-1 multilevel mediation analysis model in R: A replication of Bauer, Preacher, and Gil (2006)

Bauer, Preacher, and Gil (2006) developed a popular estimation approach for the 1-1-1 multilevel mediation analysis model, using simulations to evaluate the performance of two computationally efficient ways to obtain intervals for the indirect effect. While the model can be estimated in a variety of software packages, support in R lags behind as the original approaches to interval estimation were demonstrated using commercial software. Recent research with R instead has only demonstrated interval estimation with more computationally intensive methods. Meanwhile, other recent work has focused attention towards how Monte Carlo simulation studies are conducted and reported, highlighting the importance of replicating previous findings. Our goals in this manuscript are twofold. First, we show how to implement the original computationally efficient interval estimation methods for the 1-1-1 multilevel mediation analysis model in R. We do so by using the Delta method to obtain elements of the asymptotic covariance matrix among model parameters necessary for these approaches. Second, in a pre-registered study, we evaluate our implementation by attempting to partially replicate the original simulation study by Bauer et al. (2006). In general, our results indicate that our implementation is operating as expected as Type I error rates and coverage were acceptable when assumptions were met. Furthermore, though we observed higher convergence rates, the major findings from Bauer et al. (2006) were replicated. We hope that extensions to this work will help lead to more advanced multilevel mediation analysis models being readily available to applied researchers.