TY - JOUR
T1 - Parametric links for binary choice models
T2 - A Fisherian-Bayesian colloquy
AU - Koenker, Roger
AU - Yoon, Jungmo
N1 - Funding Information:
This research was partially supported NSF grant SES-05-44673. The authors, while retaining full culpability for any errors and misconceptions, would like to express their appreciation to Victor Chernozhukov, Trevor Hastie, Stephen Portnoy and an anonymous referee for valuable comments.
PY - 2009/10
Y1 - 2009/10
N2 - 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.
AB - 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.
KW - Binary response model
KW - Cauchit
KW - Link function
KW - Markov chain Monte-Carlo
UR - http://www.scopus.com/inward/record.url?scp=68949220402&partnerID=8YFLogxK
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U2 - 10.1016/j.jeconom.2009.01.009
DO - 10.1016/j.jeconom.2009.01.009
M3 - Article
AN - SCOPUS:68949220402
SN - 0304-4076
VL - 152
SP - 120
EP - 130
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -