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Article: Bayesian analysis of errors-in-variables in binary regression models
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TitleBayesian analysis of errors-in-variables in binary regression models
 
AuthorsTang, PK
Bacon-Shone, J
 
KeywordsErrors-in-variables
Binary regression
Bayesian inference
Loss function
Non-informative prior
 
Issue Date1992
 
PublisherUniversity of Hong Kong. Dept. of Statistics.
 
CitationResearch 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.
 
DC FieldValue
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
 
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.
 
dc.description.naturepostprint
 
dc.identifier.citationResearch Report, n. 12, p. 1-32 [How to Cite?]
 
dc.identifier.urihttp://hdl.handle.net/10722/60986
 
dc.language.isoeng
 
dc.publisherUniversity of Hong Kong. Dept. of Statistics.
 
dc.rightsAuthor holds the copyright
 
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License
 
dc.subjectErrors-in-variables
 
dc.subjectBinary regression
 
dc.subjectBayesian inference
 
dc.subjectLoss function
 
dc.subjectNon-informative prior
 
dc.titleBayesian analysis of errors-in-variables in binary regression models
 
dc.typeArticle
 
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<contributor.author>Bacon-Shone, J</contributor.author>
<date.accessioned>2010-06-02T06:34:56Z</date.accessioned>
<date.available>2010-06-02T06:34:56Z</date.available>
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<description.abstract>There 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&apos;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.</description.abstract>
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<publisher>University of Hong Kong. Dept. of Statistics.</publisher>
<rights>Author holds the copyright</rights>
<rights>Creative Commons: Attribution 3.0 Hong Kong License</rights>
<subject>Errors-in-variables</subject>
<subject>Binary regression</subject>
<subject>Bayesian inference</subject>
<subject>Loss function</subject>
<subject>Non-informative prior</subject>
<title>Bayesian analysis of errors-in-variables in binary regression models</title>
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