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Article: Bayesian analysis of errors-in-variables in binary regression models

TitleBayesian analysis of errors-in-variables in binary regression models
Authors
KeywordsErrors-in-variables
Binary regression
Bayesian inference
Loss function
Non-informative prior
Issue DateMay-1992
PublisherUniversity of Hong Kong. Dept. of Statistics.
Citation
Research Report, n. 12, p. 1-32 How to Cite?
AbstractThere has been considerable research done on the problems of errors-in-variables for linear regression. including a Bayesian solution by Lindley and EI-Sayyad (1968). Recently, interest has extended to binary regression and in particular probit regression. Burr (1985) performed frequentist analysis of Berkson's error in probit regression and found that the MLE does not ,always exist in finite samples. In this paper. we show that it is the tail behaviour of the likelihood that causes the problem and this in turn makes Bayesian estimation inadmissible if improper priors are used. Two non-informative priors are derived and simulation results indicate that the Bayesian solutions are generally superior to various likelihood based estimates, including the modified MLE proposed by Burr. It is further shown that the estimation problem vanishes if there are replicates and that the logistic model has the same behaviour as the probit model.
Persistent Identifierhttp://hdl.handle.net/10722/60986

 

DC FieldValueLanguage
dc.contributor.authorTang, PK-
dc.contributor.authorBacon-Shone, J-
dc.date.accessioned2010-06-02T06:34:56Z-
dc.date.available2010-06-02T06:34:56Z-
dc.date.issued1992-05-
dc.identifier.citationResearch Report, n. 12, p. 1-32en_HK
dc.identifier.urihttp://hdl.handle.net/10722/60986-
dc.description.abstractThere has been considerable research done on the problems of errors-in-variables for linear regression. including a Bayesian solution by Lindley and EI-Sayyad (1968). Recently, interest has extended to binary regression and in particular probit regression. Burr (1985) performed frequentist analysis of Berkson's error in probit regression and found that the MLE does not ,always exist in finite samples. In this paper. we show that it is the tail behaviour of the likelihood that causes the problem and this in turn makes Bayesian estimation inadmissible if improper priors are used. Two non-informative priors are derived and simulation results indicate that the Bayesian solutions are generally superior to various likelihood based estimates, including the modified MLE proposed by Burr. It is further shown that the estimation problem vanishes if there are replicates and that the logistic model has the same behaviour as the probit model.en_HK
dc.language.isoengen_HK
dc.publisherUniversity of Hong Kong. Dept. of Statistics.en_HK
dc.rightsAuthor holds the copyright-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectErrors-in-variablesen_HK
dc.subjectBinary regressionen_HK
dc.subjectBayesian inferenceen_HK
dc.subjectLoss functionen_HK
dc.subjectNon-informative prior-
dc.titleBayesian analysis of errors-in-variables in binary regression modelsen_HK
dc.typeArticleen_HK
dc.description.naturepostprint-

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