### Abstract

Original language | English |
---|---|

Pages (from-to) | 229-261 |

Journal | British Journal of Mathematical and Statistical Psychology |

Volume | 71 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- CONSISTENCY
- DIMENSION
- INEQUALITY CONSTRAINED HYPOTHESES
- LINEAR-MODELS
- MODEL SELECTION
- PRIOR DISTRIBUTIONS
- RATIO
- VARIABLE SELECTION
- fractional Bayes factor
- informative hypothesis
- normal approximation
- prior sensitivity

### Cite this

*British Journal of Mathematical and Statistical Psychology*,

*71*(2), 229-261. https://doi.org/10.1111/bmsp.12110

}

*British Journal of Mathematical and Statistical Psychology*, vol. 71, no. 2, pp. 229-261. https://doi.org/10.1111/bmsp.12110

**Approximated adjusted fractional Bayes factors : A general method for testing informative hypotheses.** / Gu, X.; Mulder, J.; Hoijtink, H.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Approximated adjusted fractional Bayes factors

T2 - A general method for testing informative hypotheses

AU - Gu, X.

AU - Mulder, J.

AU - Hoijtink, H.

PY - 2018

Y1 - 2018

N2 - Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure.

AB - Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure.

KW - CONSISTENCY

KW - DIMENSION

KW - INEQUALITY CONSTRAINED HYPOTHESES

KW - LINEAR-MODELS

KW - MODEL SELECTION

KW - PRIOR DISTRIBUTIONS

KW - RATIO

KW - VARIABLE SELECTION

KW - fractional Bayes factor

KW - informative hypothesis

KW - normal approximation

KW - prior sensitivity

U2 - 10.1111/bmsp.12110

DO - 10.1111/bmsp.12110

M3 - Article

VL - 71

SP - 229

EP - 261

JO - British Journal of Mathematical and Statistical Psychology

JF - British Journal of Mathematical and Statistical Psychology

SN - 0007-1102

IS - 2

ER -