A tutorial on Bayesian multi-model linear regression with BAS and JASP.

Journal Article (Journal Article)

Linear regression analyses commonly involve two consecutive stages of statistical inquiry. In the first stage, a single 'best' model is defined by a specific selection of relevant predictors; in the second stage, the regression coefficients of the winning model are used for prediction and for inference concerning the importance of the predictors. However, such second-stage inference ignores the model uncertainty from the first stage, resulting in overconfident parameter estimates that generalize poorly. These drawbacks can be overcome by model averaging, a technique that retains all models for inference, weighting each model's contribution by its posterior probability. Although conceptually straightforward, model averaging is rarely used in applied research, possibly due to the lack of easily accessible software. To bridge the gap between theory and practice, we provide a tutorial on linear regression using Bayesian model averaging in JASP, based on the BAS package in R. Firstly, we provide theoretical background on linear regression, Bayesian inference, and Bayesian model averaging. Secondly, we demonstrate the method on an example data set from the World Happiness Report. Lastly, we discuss limitations of model averaging and directions for dealing with violations of model assumptions.

Full Text

Duke Authors

Cited Authors

  • Bergh, DVD; Clyde, MA; Gupta, ARKN; de Jong, T; Gronau, QF; Marsman, M; Ly, A; Wagenmakers, E-J

Published Date

  • December 2021

Published In

Volume / Issue

  • 53 / 6

Start / End Page

  • 2351 - 2371

PubMed ID

  • 33835394

Pubmed Central ID

  • PMC8613115

Electronic International Standard Serial Number (EISSN)

  • 1554-3528

International Standard Serial Number (ISSN)

  • 1554-351X

Digital Object Identifier (DOI)

  • 10.3758/s13428-021-01552-2

Language

  • eng