Bayesian multilevel models are increasingly used to overcome the limitations of frequentist approaches in the analysis of complex structured data. This tutorial introduces Bayesian multilevel modeling for the specific analysis of speech data, using the brms package developed in R. In this tutorial, we provide a practical introduction to Bayesian multilevel modeling by reanalyzing a phonetic data set containing formant (F1 and F2) values for 5 vowels of standard Indonesian (ISO 639-3:ind), as spoken by 8 speakers (4 females and 4 males), with several repetitions of each vowel. We first give an introductory overview of the Bayesian framework and multilevel modeling. We then show how Bayesian multilevel models can be fitted using the probabilistic programming language Stan and the R package brms, which provides an intuitive formula syntax. Through this tutorial, we demonstrate some of the advantages of the Bayesian ramework for statistical modeling and provide a detailed case study, with complete source code for full reproducibility of the analyses.
In light of current concerns with replicability and reporting false-positive effects in psychology, we examine Type I errors and power associated with 2 distinct approaches for the assessment of mediation, namely the component approach (testing individual parameter estimates in the model) and the index approach (testing a single mediational index). We conduct simulations that examine both approaches and show that the most commonly used tests under the index approach risk inflated Type I errors compared with the joint-significance test inspired by the component approach. We argue that the tendency to report only a single mediational index is worrisome for this reason and also because it is often accompanied by a failure to critically examine the individual causal paths underlying the mediational model. We recommend testing individual components of the indirect effect to argue for the presence of an indirect effect and then using other recommended procedures to calculate the size of that effect. Beyond simple mediation, we show that our conclusions also apply in cases of within-participant mediation and moderated mediation. We also provide a new R-package that allows for an easy implementation of our recommendations.