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A default prior for regression coefficients.

ABSTRACT: When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-informative. In spite of this, we argue that the uniform prior is not suitable as a default prior for inference about a regression coefficient in the context of the bio-medical and social sciences. We propose that a more suitable default choice is the normal distribution with mean zero and standard deviation equal to the standard error of the M-estimator. We base this recommendation on two arguments. First, we show that this prior is non-informative for inference about the sign of the regression coefficient. Second, we show that this prior agrees well with a meta-analysis of 50 articles from the MEDLINE database.

SUBMITTER: van Zwet E

PROVIDER: S-EPMC6745606 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

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A default prior for regression coefficients.

van Zwet Erik E

Statistical methods in medical research 20181213 12

When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and <i>p</i>-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-info ...[more]

PMID: 30543154

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