Parametric links for binary choice models: A Fisherian-Bayesian colloquy

Roger Koenker, Jungmo Yoon

Research output: Contribution to journalArticlepeer-review


The familiar logit and probit models provide convenient settings for many binary response applications, but a larger class of link functions may be occasionally desirable. Two parametric families of link functions are investigated: the Gosset link based on the Student t latent variable model with the degrees of freedom parameter controlling the tail behavior, and the Pregibon link based on the (generalized) Tukey λ family, with two shape parameters controlling skewness and tail behavior. Both Bayesian and maximum likelihood methods for estimation and inference are explored, compared and contrasted. In applications, like the propensity score matching problem discussed below, where it is critical to have accurate estimates of the conditional probabilities, we find that misspecification of the link function can create serious bias. Bayesian point estimation via MCMC performs quite competitively with MLE methods; however nominal coverage of Bayes credible regions is somewhat more problematic.

Original languageEnglish (US)
Pages (from-to)120-130
Number of pages11
JournalJournal of Econometrics
Issue number2
StatePublished - Oct 2009


  • Binary response model
  • Cauchit
  • Link function
  • Markov chain Monte-Carlo

ASJC Scopus subject areas

  • Economics and Econometrics


Dive into the research topics of 'Parametric links for binary choice models: A Fisherian-Bayesian colloquy'. Together they form a unique fingerprint.

Cite this