# Bain

Bain is an abbreviation for BAyesian INequality and equality constrained hypothesis evaluation. It uses the Bayes factor to evaluate hypotheses in a wide variety of statistical models. One example are the hypotheses H1: m1 = m2 = m3, H2: m1 > m2 > m3, and Hu: m1, m2, m3 (no constraints) where m1, m2, and m3 denote the means in an ANOVA model. Another example is the hypothesis H1: b1 > 0, b2 > 0, b1 > b2 and its complement Hc: not H1, where b1 and b2 denote standardized regression coefficients.

Bain was developed and is being maintained by:

Department of Geography and Planning

University of Liverpool – GuXin57@hotmail.com

Herbert Hoijtink

Department of Methodology and Statistics

Utrecht University – H.Hoijtink@uu.nl

Joris Mulder

Department of Methodology and Statistics

Tilburg University – J.Mulder3@uvt.nl

The following persons have contributed to the further development and presentation of Bain:

The R package Bain can be used for the evaluation of classical and informative hypotheses using the Bayes factor. BaIn is licensed under the GNU General Public License Version >=3 The current version is Bain-0.1.1 It is a beta version, that is, there may still be errors and bugs in the package. Let us know if you find one.

**CLICK HERE** to obtain all Bain versions released previous to Bain-0.1.1. The first one is the Fortran90 version used in Xin Gu’s dissertation and the publication in the British Journal of Mathematical and Statistical Psychology. The second one is Bain-0.1.0.

**CLICK HERE to obtain Bain-0.1.1**, installation instructions for Windows, Mac, and Linux, **UNDER R-3.4.x OR EARLIER** and the tutorial explaining how to evaluate classical and informative hypotheses using the Bayes factor. You are well advised to read the tutorial before using Bain. **NOTE: ****the call to Bain has been changed (see the examples); error messages have been improved; and functions facilitating the use of the t-test, ANOVA, ANCOVA, and Multiple Regression have been added (see the examples).**

**CLICK HERE to obtain Bain-0.1.1**, installation instructions for Windows, Mac, and Linux, **UNDER R-3.5.x **and the tutorial explaining how to evaluate classical and informative hypotheses using the Bayes factor. You are well advised to read the tutorial before using Bain. **NOTE: ****the call to Bain has been changed (see the examples); error messages have been improved; and functions facilitating the use of the t-test, ANOVA, ANCOVA, and Multiple Regression have been added (see the examples).**

**EXAMPLES OF USING BAIN IN THE CONTEXT OF VARIOUS STATISTICAL MODELS **additional examples will be added in the course of 2018 and 2019. *The first four items in the list will be implemented in ***JASP**

*Is your application not included in the list and you want support, send an e-mail to H.Hoijtink@uu.nl and include the model you want to use, your hypotheses, and data. **You can also invite us to give a workshop based on the material covered in workshopslides.pdf*

*Click to download example R code and description*

- The independent samples
**t-test**with unequal variances per group **ANOVA**see also tutorial.pdf and BFTutorial.R as included in the Bain download**ANCOVA****Multiple Regression****equivalence testing****Multiple Group Logistic Regression****Multiple Regression when the Data Contain Missing Values****Repeated Measures in a Within Between Design****Robust ANOVA**by Marlyne Bosman

**You can give credit to the authors of Bain by referring to:
**

Gu, X., Mulder, J., and Hoijtink, H. (in press). Approximate adjusted fractional Bayes factors: A general method for testing informative hypotheses. British Journal of Mathematical and Statistical Psychology. **DOI:** 10.1111/bmsp.12110

Hoijtink, H., Gu, X., and Mulder, J. (unpublished). Bayesian Evaluation of Informative Hypotheses for Multiple Populations. With here the Online supplementary materials

**Other important publications are:**

Gu, X. (2016). Bayesian Evaluation of Informative Hypotheses. Doctoral Dissertation, University Utrecht.

Hoijtink, H., Gu, X., Mulder, J., and Rosseel, Y. (in press). Computing Bayes Factors from Data with Missing Values. Psychological Methods. **DOI: 10.1037/met0000187** ** **Online Supplementary Materials (**BASED ON BAIN-0.1.0!!)**