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Bayesian inference in the multivariate probit model Tabet, Aline
Abstract
Correlated binary data arise in many applications. Any analysis of this type of data should take into account the correlation structure among the variables. The multivariate Probit model (MVP), introduced by Ashford and Snowden (1970), is a popular class of models particularly suitable for the analysis of correlated binary data. In this class of models, the response is multivariate, correlated and discrete. Generally speaking, the MVP model assumes that given a set of explanatory variables the multivariate response is an indicator of the event that some unobserved latent variable falls within a certain interval. The latent variable is assumed to arise from a multivariate normal distribution. Difficulties with the multivariate Probit are mainly due to computation as the likelihood of the observed discrete data is obtained by integrating over a multidimensional constrained space of latent variables. In this work, we adopt a Bayesian approach and develop an an efficient Markov chain Monte Carlo algorithm for estimation in MVP models under the full correlation and the structured correlation assumptions. Furthermore, in addition to simulation results, we present an application of our method to the Six Cities data set. Our algorithm has many advantages over previous approaches, namely it handles identifiability and uses a marginally uniform prior on the correlation matrix directly.
Item Metadata
Title |
Bayesian inference in the multivariate probit model
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2007
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Description |
Correlated binary data arise in many applications. Any analysis of this
type of data should take into account the correlation structure among the
variables. The multivariate Probit model (MVP), introduced by Ashford
and Snowden (1970), is a popular class of models particularly suitable for
the analysis of correlated binary data. In this class of models, the response is
multivariate, correlated and discrete. Generally speaking, the MVP model
assumes that given a set of explanatory variables the multivariate response is
an indicator of the event that some unobserved latent variable falls within a
certain interval. The latent variable is assumed to arise from a multivariate
normal distribution. Difficulties with the multivariate Probit are mainly due
to computation as the likelihood of the observed discrete data is obtained by
integrating over a multidimensional constrained space of latent variables. In
this work, we adopt a Bayesian approach and develop an an efficient Markov
chain Monte Carlo algorithm for estimation in MVP models under the full
correlation and the structured correlation assumptions. Furthermore, in
addition to simulation results, we present an application of our method to
the Six Cities data set. Our algorithm has many advantages over previous
approaches, namely it handles identifiability and uses a marginally uniform
prior on the correlation matrix directly.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-03-09
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0101129
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.