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A Bayesian goodness-of-fit test for regression

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  • Barrientos, Andrés F.
  • Canale, Antonio

Abstract

Regression models are widely used statistical procedures, and the validation of their assumptions plays a crucial role in the data analysis process. Unfortunately, validating assumptions usually depends on the availability of tests tailored to the specific model of interest. A novel Bayesian goodness-of-fit hypothesis testing approach is presented for a broad class of regression models the response variable of which is univariate and continuous. The proposed approach relies on a suitable transformation of the response variable and a Bayesian prior induced by a predictor-dependent mixture model. Hypothesis testing is performed via Bayes factor, the asymptotic properties of which are discussed. The method is implemented by means of a Markov chain Monte Carlo algorithm, and its performance is illustrated using simulated and real data sets.

Suggested Citation

  • Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:csdana:v:155:y:2021:i:c:s016794732030195x
    DOI: 10.1016/j.csda.2020.107104
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