Simple and flexible Bayesian inferences for standardized regression coefficients

Yonggang Lu, Peter Westfall

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In statistical practice, inferences on standardized regression coefficients are often required, but complicated by the fact that they are nonlinear functions of the parameters, and thus standard textbook results are simply wrong. Within the frequentist domain, asymptotic delta methods can be used to construct confidence intervals of the standardized coefficients with proper coverage probabilities. Alternatively, Bayesian methods solve similar and other inferential problems by simulating data from the posterior distribution of the coefficients. In this paper, we present Bayesian procedures that provide comprehensive solutions for inferences on the standardized coefficients. Simple computing algorithms are developed to generate posterior samples with no autocorrelation and based on both noninformative improper and informative proper prior distributions. Simulation studies show that Bayesian credible intervals constructed by our approaches have comparable and even better statistical properties than their frequentist counterparts, particularly in the presence of collinearity. In addition, our approaches solve some meaningful inferential problems that are difficult if not impossible from the frequentist standpoint, including identifying joint rankings of multiple standardized coefficients and making optimal decisions concerning their sizes and comparisons. We illustrate applications of our approaches through examples and make sample R functions available for implementing our proposed methods.

Original languageEnglish
Pages (from-to)2254-2288
Number of pages35
JournalJournal of Applied Statistics
Issue number12
StatePublished - Sep 10 2019


  • Bayesian posterior sampling
  • Standardized regression coefficient
  • decision analysis
  • frequentist coverage property
  • multiple comparisons


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