Abstract
Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters (regression coefficients) in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions.
Highlights
Informative prior distributions are a crucial element of Bayesian statistics, and play a pivotal role for scientific disciplines that aim at constructing a cumulative knowledge base
The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions
The results of our simulation show that the parameter estimates of the similarity-weighted informative prior distribution behave similar to those of hierarchical Bayesian models: as the similarity of the focal and previously conducted studies increases, they shrink toward their pooled, meta-analytic means
Summary
Informative prior distributions are a crucial element of Bayesian statistics, and play a pivotal role for scientific disciplines that aim at constructing a cumulative knowledge base. Informative prior distributions are background knowledge quantified and introduced in a Bayesian analysis. Their use allows studies to build upon each other, to update the knowledge base of a scientific discipline. This is a central tenet of the new statistics (Cumming, 2014). Despite the increase of Bayesian statistics in various scientific disciplines over the last years, the use of informative prior distributions is still relatively rare (for instance in Psychology, see van de Schoot et al, 2017; for Educational Science see König and van de Schoot, 2018). The potential of Bayesian statistics for cumulative science is not fully realized yet
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