### Abstract

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

Pages (from-to) | 253-268 |

Journal | Psychological Methods |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 |

### Fingerprint

### Keywords

- Bayes Factor
- INEQUALITY
- MARGINAL LIKELIHOOD
- MULTIPLE-IMPUTATION
- informative hypotheses
- missing data
- multiple imputation

### Cite this

*Psychological Methods*,

*24*(2), 253-268. https://doi.org/10.1037/met0000187

}

*Psychological Methods*, vol. 24, no. 2, pp. 253-268. https://doi.org/10.1037/met0000187

**Computing Bayes factors from data with missing values.** / Hoijtink, Herbert; Gu, Xin; Mulder, Joris; Rosseel, Y.

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

TY - JOUR

T1 - Computing Bayes factors from data with missing values

AU - Hoijtink, Herbert

AU - Gu, Xin

AU - Mulder, Joris

AU - Rosseel, Y.

PY - 2019

Y1 - 2019

N2 - The Bayes factor is increasingly used for the evaluation of hypotheses. These may be traditional hypotheses specified using equality constraints among the parameters of the statistical model of interest or informative hypotheses specified using equality and inequality constraints. Thus far, no attention has been given to the computation of Bayes factors from data with missing values. A key property of such a Bayes factor should be that it is only based on the information in the observed values. This article will show that such a Bayes factor can be obtained using multiple imputations of the missing values. After introduction of the general framework elaborations for Bayes factors based on default or subjective prior distributions and Bayes factors based on priors specified using training data will be given. It will be illustrated that the approach proposed can be applied using R packages for multiple imputation in combination with the Bayes factor packages Bain and BayesFactor. It will furthermore be illustrated that Bayes factors computed using a single imputation of the data are very inaccurate approximations of the correct Bayes factor.

AB - The Bayes factor is increasingly used for the evaluation of hypotheses. These may be traditional hypotheses specified using equality constraints among the parameters of the statistical model of interest or informative hypotheses specified using equality and inequality constraints. Thus far, no attention has been given to the computation of Bayes factors from data with missing values. A key property of such a Bayes factor should be that it is only based on the information in the observed values. This article will show that such a Bayes factor can be obtained using multiple imputations of the missing values. After introduction of the general framework elaborations for Bayes factors based on default or subjective prior distributions and Bayes factors based on priors specified using training data will be given. It will be illustrated that the approach proposed can be applied using R packages for multiple imputation in combination with the Bayes factor packages Bain and BayesFactor. It will furthermore be illustrated that Bayes factors computed using a single imputation of the data are very inaccurate approximations of the correct Bayes factor.

KW - Bayes Factor

KW - INEQUALITY

KW - MARGINAL LIKELIHOOD

KW - MULTIPLE-IMPUTATION

KW - informative hypotheses

KW - missing data

KW - multiple imputation

U2 - 10.1037/met0000187

DO - 10.1037/met0000187

M3 - Article

VL - 24

SP - 253

EP - 268

JO - Psychological Methods

JF - Psychological Methods

SN - 1082-989X

IS - 2

ER -