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There have been considerable methodological developments of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constraints on the parameters of interest, and the interpretability of the outcome as the weight of evidence provided by the data in support of competing scientific theories. The available software tools for Bayesian hypothesis testing are still limited however. In this paper we present a new R package called BFpack that contains functions for Bayes factor hypothesis testing for the many common testing problems. The software includes novel tools for (i) Bayesian exploratory testing (e.g., zero vs positive vs negative effects), (ii) Bayesian confirmatory testing (competing hypotheses with equality and/or order constraints), (iii) common statistical analyses, such as linear regression, generalized linear models, (multivariate) analysis of (co)variance, correlation analysis, and random intercept models, (iv) using default priors, and (v) while allowing data to contain missing observations that are missing at random.
Keywords
ORDER-CONSTRAINED HYPOTHESES, AREA PREDICTS FACE, INEQUALITY, IMPUTATION, THICKNESS, PRECISE, PROGRAM, MODELS, PRIORS, Bayes factors, hypothesis testing, equality/order constrained, hypotheses, R

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MLA
Mulder, Joris, et al. “BFpack : Flexible Bayes Factor Testing of Scientific Theories in R.” JOURNAL OF STATISTICAL SOFTWARE, vol. 100, no. 18, 2021, pp. 1–63, doi:10.18637/jss.v100.i18.
APA
Mulder, J., Williams, D. R., Gu, X., Tomarken, A., Boing-Messing, F., Olsson-Collentine, A., … van Lissa, C. (2021). BFpack : flexible bayes factor testing of scientific theories in R. JOURNAL OF STATISTICAL SOFTWARE, 100(18), 1–63. https://doi.org/10.18637/jss.v100.i18
Chicago author-date
Mulder, Joris, Donald R. Williams, Xin Gu, Andrew Tomarken, Florian Boing-Messing, Anton Olsson-Collentine, Marlyne Meijerink, et al. 2021. “BFpack : Flexible Bayes Factor Testing of Scientific Theories in R.” JOURNAL OF STATISTICAL SOFTWARE 100 (18): 1–63. https://doi.org/10.18637/jss.v100.i18.
Chicago author-date (all authors)
Mulder, Joris, Donald R. Williams, Xin Gu, Andrew Tomarken, Florian Boing-Messing, Anton Olsson-Collentine, Marlyne Meijerink, Janosch Menke, Robbie van Aert, Jean-Paul Fox, Herbert Hoijtink, Yves Rosseel, Eric-Jan Wagenmakers, and Caspar van Lissa. 2021. “BFpack : Flexible Bayes Factor Testing of Scientific Theories in R.” JOURNAL OF STATISTICAL SOFTWARE 100 (18): 1–63. doi:10.18637/jss.v100.i18.
Vancouver
1.
Mulder J, Williams DR, Gu X, Tomarken A, Boing-Messing F, Olsson-Collentine A, et al. BFpack : flexible bayes factor testing of scientific theories in R. JOURNAL OF STATISTICAL SOFTWARE. 2021;100(18):1–63.
IEEE
[1]
J. Mulder et al., “BFpack : flexible bayes factor testing of scientific theories in R,” JOURNAL OF STATISTICAL SOFTWARE, vol. 100, no. 18, pp. 1–63, 2021.
@article{8737587,
  abstract     = {{There have been considerable methodological developments of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constraints on the parameters of interest, and the interpretability of the outcome as the weight of evidence provided by the data in support of competing scientific theories. The available software tools for Bayesian hypothesis testing are still limited however. In this paper we present a new R package called BFpack that contains functions for Bayes factor hypothesis testing for the many common testing problems. The software includes novel tools for (i) Bayesian exploratory testing (e.g., zero vs positive vs negative effects), (ii) Bayesian confirmatory testing (competing hypotheses with equality and/or order constraints), (iii) common statistical analyses, such as linear regression, generalized linear models, (multivariate) analysis of (co)variance, correlation analysis, and random intercept models, (iv) using default priors, and (v) while allowing data to contain missing observations that are missing at random.}},
  author       = {{Mulder, Joris and Williams, Donald R. and Gu, Xin and Tomarken, Andrew and Boing-Messing, Florian and Olsson-Collentine, Anton and Meijerink, Marlyne and Menke, Janosch and van Aert, Robbie and Fox, Jean-Paul and Hoijtink, Herbert and Rosseel, Yves and Wagenmakers, Eric-Jan and van Lissa, Caspar}},
  issn         = {{1548-7660}},
  journal      = {{JOURNAL OF STATISTICAL SOFTWARE}},
  keywords     = {{ORDER-CONSTRAINED HYPOTHESES,AREA PREDICTS FACE,INEQUALITY,IMPUTATION,THICKNESS,PRECISE,PROGRAM,MODELS,PRIORS,Bayes factors,hypothesis testing,equality/order constrained,hypotheses,R}},
  language     = {{eng}},
  number       = {{18}},
  pages        = {{1--63}},
  title        = {{BFpack : flexible bayes factor testing of scientific theories in R}},
  url          = {{http://dx.doi.org/10.18637/jss.v100.i18}},
  volume       = {{100}},
  year         = {{2021}},
}

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