Before/after Bayes: A comparison of frequentist and Bayesian mixed‐effects models in applied psychological research

Abstract

Bayesian methods are becoming increasingly used in applied psychological research. Previous researchers have thoroughly written about much of the details already, including the philosophy underlying Bayesian methods, computational issues associated with Bayesian model estimation, Bayesian model development and summary, and the role of Bayesian methods in the so‐called replication crisis. In this paper, we seek to provide case studies comparing the use of frequentist methods to the use of Bayesian methods in applied psychological research. These case studies are intended to ‘illustrate by example’ the ways that Bayesian modelling differs from frequentist modelling and the differing conclusions that one may arrive at using the two methods. The intended audience is applied psychological researchers who have been trained in the traditional frequentist framework, who are familiar with mixed‐effects models and who are curious about how statistical results might look in a Bayesian context. Along with our case studies, we provide general opinions and guidance on the use of Bayesian methods in applied psychological research.

Keeping the promise: a critique of the current state of microdosing research

“…Marschall et al ( 17 ) reported both frequentist and Bayesian analyses, noting that only the former were pre-registered but that the latter add more nuance in quantifying the relative evidence. While using a mix of frequentist and Bayesian analyses is increasingly a standard best-practice in psychological research ( 62 ), this study is the only one in the literature using this best practice. The paper also adequately reports which trials were excluded (e.g., go/no-go task responses above two standard deviations from the participant’s average).…”

Gender Dysphoria and Sexual Euphoria: A Bayesian Perspective on the Influence of Gender-Affirming Hormone Therapy on Sexual Arousal

“…Bayesian multilevel models further protect against multiplicity issues (Gelman et al, 2012 ), which would have arisen for frequentist comparisons of four groups and two time points, allowing for more in-depth inferences. See Flores et al ( 2022 ) for a detailed comparison of frequentist versus Bayesian mixed models and the supplement for a complementary frequentist analysis.…”

“…Here we assess changes to brain measures of sexual arousal related to transition using fMRI, focusing on the VS, based on previous reports of its specific role in this function (Safron et al, 2007 , 2017 , 2020 ; Sylva et al, 2013 ; Walter et al, 2008 ). We hypothesized that the patterns of behavioral responses and VS activation to erotic stimuli shift from assigned to experienced gender over the course of GHT, in analogy to patterns detected using other MRI based outcome parameters, such as white and gray matter structure (Flores et al, 2022 ; Kilpatrick et al, 2019 ; Kranz et al, 2017 , 2018 ). To this aim, we assessed the subjective arousal ratings and VS activation in a sample of TW and TM before and after four months of GHT as well as CW and CM control groups, all undergoing an fMRI sexual arousal task.…”