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

Publication ,  Journal Article
Bergh, DVD; Clyde, MA; Gupta, ARKN; de Jong, T; Gronau, QF; Marsman, M; Ly, A; Wagenmakers, E-J
Published in: Behavior research methods
December 2021

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.

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Published In

Behavior research methods

DOI

EISSN

1554-3528

ISSN

1554-351X

Publication Date

December 2021

Volume

53

Issue

6

Start / End Page

2351 / 2371

Related Subject Headings

  • Software
  • Research Design
  • Regression Analysis
  • Linear Models
  • Experimental Psychology
  • Bayes Theorem
  • 5204 Cognitive and computational psychology
  • 5202 Biological psychology
  • 4905 Statistics
  • 1702 Cognitive Sciences
 

Citation

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Bergh, D. V. D., Clyde, M. A., Gupta, A. R. K. N., de Jong, T., Gronau, Q. F., Marsman, M., … Wagenmakers, E.-J. (2021). A tutorial on Bayesian multi-model linear regression with BAS and JASP. Behavior Research Methods, 53(6), 2351–2371. https://doi.org/10.3758/s13428-021-01552-2
Bergh, Don van den, Merlise A. Clyde, Akash R Komarlu Narendra Gupta, Tim de Jong, Quentin F. Gronau, Maarten Marsman, Alexander Ly, and Eric-Jan Wagenmakers. “A tutorial on Bayesian multi-model linear regression with BAS and JASP.Behavior Research Methods 53, no. 6 (December 2021): 2351–71. https://doi.org/10.3758/s13428-021-01552-2.
Bergh DVD, Clyde MA, Gupta ARKN, de Jong T, Gronau QF, Marsman M, et al. A tutorial on Bayesian multi-model linear regression with BAS and JASP. Behavior research methods. 2021 Dec;53(6):2351–71.
Bergh, Don van den, et al. “A tutorial on Bayesian multi-model linear regression with BAS and JASP.Behavior Research Methods, vol. 53, no. 6, Dec. 2021, pp. 2351–71. Epmc, doi:10.3758/s13428-021-01552-2.
Bergh DVD, Clyde MA, Gupta ARKN, de Jong T, Gronau QF, Marsman M, Ly A, Wagenmakers E-J. A tutorial on Bayesian multi-model linear regression with BAS and JASP. Behavior research methods. 2021 Dec;53(6):2351–2371.
Journal cover image

Published In

Behavior research methods

DOI

EISSN

1554-3528

ISSN

1554-351X

Publication Date

December 2021

Volume

53

Issue

6

Start / End Page

2351 / 2371

Related Subject Headings

  • Software
  • Research Design
  • Regression Analysis
  • Linear Models
  • Experimental Psychology
  • Bayes Theorem
  • 5204 Cognitive and computational psychology
  • 5202 Biological psychology
  • 4905 Statistics
  • 1702 Cognitive Sciences