Objective Bayesian model selection approach to the two way analysis of variance
| Autor: | Diego Salmerón, Juan Antonio Cano, C. Carazo |
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| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Heteroscedasticity 010102 general mathematics Bayesian probability Two-way analysis of variance Bayes factor Bayesian inference 01 natural sciences 010104 statistics & probability Computational Mathematics Homoscedasticity Prior probability Statistics Econometrics p-value 0101 mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Computational Statistics. 33:235-248 |
| ISSN: | 1613-9658 0943-4062 |
| DOI: | 10.1007/s00180-017-0727-1 |
| Popis: | An objective Bayesian procedure for testing in the two way analysis of variance is proposed. In the classical methodology the main effects of the two factors and the interaction effect are formulated as linear contrasts between means of normal populations, and hypotheses of the existence of such effects are tested. In this paper, for the first time these hypotheses have been formulated as objective Bayesian model selection problems. Our development is under homoscedasticity and heteroscedasticity, providing exact solutions in both cases. Bayes factors are the key tool to choose between the models under comparison but for the usual default prior distributions they are not well defined. To avoid this difficulty Bayes factors for intrinsic priors are proposed and they are applied in this setting to test the existence of the main effects and the interaction effect. The method has been illustrated with an example and compared with the classical method. For this example, both approaches went in the same direction although the large P value for interaction (0.79) only prevents us against to reject the null, and the posterior probability of the null (0.95) was conclusive. |
| Databáze: | OpenAIRE |
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