JiscMail Logo
Email discussion lists for the UK Education and Research communities

Help for BUGS Archives


BUGS Archives

BUGS Archives


BUGS@JISCMAIL.AC.UK


View:

Message:

[

First

|

Previous

|

Next

|

Last

]

By Topic:

[

First

|

Previous

|

Next

|

Last

]

By Author:

[

First

|

Previous

|

Next

|

Last

]

Font:

Monospaced Font

LISTSERV Archives

LISTSERV Archives

BUGS Home

BUGS Home

BUGS  February 2007

BUGS February 2007

Options

Subscribe or Unsubscribe

Subscribe or Unsubscribe

Log In

Log In

Get Password

Get Password

Subject:

Summary: multivariate probit model

From:

[log in to unmask]

Reply-To:

[log in to unmask]

Date:

Wed, 28 Feb 2007 01:37:44 -0500

Content-Type:

TEXT/PLAIN

Parts/Attachments:

Parts/Attachments

TEXT/PLAIN (185 lines)

Dear WinBUGS users:

Last week, I asked for advice on how to implement a multivariate probit
model (with 3 equations).

I received many helpful answers. I pasted them below.

I truly thank all those who offered advice for their generous support and
their insightful suggestions. I am working my way through them.

Best regards,
giacomo


##############################################################

1.

You can place a Wishart prior on the precision matrix. This will give you
an estimate of the sigma matrix. You can then use the sigmas to scale the
regression coefficients to obtain probit coeffcients. This is consistent
with Chib and Greenberg who write: "Suppose that (gamma, Q) is an
alternative
parameterisation, where gamma is the regression parameter vector and Q is
the covariance matrix. Then it is easy to show that
pr(y|gamma, Q) = pr(y|beta, Sigma), where beta[j] = (q[jj])^-.5*gamma[j],
Sigma = CQC and C = diag{q[11]^-.5, ..., q[JJ]^-.5}.

From your code:

df <- 3
omega[1:3,1:3] ~ dwish(R[ , ], df)
sigma[1:3,1:3] <- inverse(omega[,])

for (j in 1:3) {
for (k in 1:3) {
bstar[j,k] <- b[j,k]/sqrt(sigma[j,j])
}
}


################################################################

2.

Isn't the matrix guaranteed to be positive definite? I guess the
problem is that you are getting correlations that are very close to 1
or -1, and then the numerical routine used to invert the matrix fails.

Have you tried to use a more informative prior for your
correlations? Maybe start with a Beta(20,20) and see if it runs.
And then start decreasing the parameters of the beta. Another option
might be to try to hard code the inversion of the correlation matrix,
if you are only interested in the trivariate probit model.


#################################################################

3.

This might help....

van den Berg SM, Setiawan A, Bartels M, Polderman TJ, van der Vaart AW,
Boomsma
DI. 2006 Individual differences in puberty onset in girls: Bayesian
estimation
of heritabilities and genetic correlations.
Behav Genet. 2006 Mar;36(2):261-70.


#####################################################################

4.

I may have missed something but can you orthogonalize (Cholesky?) to
three univariate normals and then transform back?  That's typically how
you generate samples from a MVN in any case, I think, so BUGs should like
it.

It shouldn't be too bad for a 3x3.


#######################################################################

5.

Practically, probit model with full variance-covariance matrix is
normalised by
setting one of the diagonal elements in the covariance matrix of error
differences to 1. To my understanding, your code seemed to set all the
diagonal
elements of the covariance matrix to 1.

Try Robert E. McCulloch, Nicholas G. Polson and Peter E. Rossi (2000) A
Bayesian analysis of the multinomial probit model with fully identified
parameters, Journal of Econometrics, Vol.99 (1), 173-193.
and the follow-up comment and response on Vol.99 (2)


########################################################################

6.

The problem is that you have allowed the covariance to not have row
diagonal
dominance. An easy fix is to let the covariances range form -.499999 to
.499999. If the sum of the absolute values of the off diagonal elements of
a
row are less than the absolute value of the diagonal element, then the
matrix is
non-singular. Nonsingular covariance matirces should have this property. I
think it is a similar criterion to the Cauchy Swartz rule that forces the
correlation between -1 and 1.


#########################################################################

7.

One idea,

Let x1, x2, x3 be three i.i.d. N(0,1) random variables,
Now let a1, a2, a3 be three vectors with three elements. Also let a1, a2
and
a3 lie on a unit sphere, then
x1*a1,x2*a2,x3*a3 are three MVN random vectors of length three with unit
variances. These vectors span the space of all possible MVN random vectors
with unit variances.

Now, without loss of generality the covariance matrix is orthogonal, so
that
any rigid rotation applied equally to all a1, a2 and a3 would give the
same
transformations. So we transform a1 = a11,0,0, a2= a21,a22,0 and
a3=a31,a32,a33 as the transformation has at least two dimensions.
Since the rotation is rigid, the new vectors also lie on the unit sphere.
The rotation is as follows. First pick a vector and rotate the frame so
that
this vector is just 1,0,0. Next rotate the frame around this vector so the
second vector lies in the x,y plane, the we can express the three vectors
(at least one way), using say spherical coordinates.

Using spherical coordinates, let
a11=1,
a21=cos(c1), a22= sin(c1),
a31=cos(c2)*cos(c3), a32=sin(c2)*cos(c3) and a33=sin(c3)

e.g.

a1=c(1,0,0)
a2=c(cos(c1),sin(c1),0)
a3=c(cos(c2)*cos(c3), sin(c2)*cos(c3),sin(c3))

The correlations are:

cor(ai,ai)=1
cor(a1,a2)=cos(c1)
cor(a1,a3)=cos(c2)*cos(c3)
cor(a2,a3)=cos(c1)*cos(c2)*cos(c3)+sin(c1)*sin(c2)*cos(c3)

So I would try

pi<-3.1415926
c1~dunif(-pi,pi)
c2~dunif(-pi,pi)
c30~dflat(-1,1)
c3<-asin(c30) ###This gives uniform distribution of a3 on sphere.

rho[1]<-cos(c1)
rho[2]<-cos(c2)*cos(c3)
rho[3]<-cos(c1)*cos(c2)*cos(c3)+sin(c1)*sin(c2)*cos(c3)

I hope this helps. I have not had time to try it out.
Since the rotations are not unique, you can have other rho values.
This might do for a start.

-------------------------------------------------------------------
This list is for discussion of modelling issues and the BUGS software.
For help with crashes and error messages, first mail [log in to unmask]
To mail the BUGS list, mail to [log in to unmask]
Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
Please do not mail attachments to the list.
To leave the BUGS list, send LEAVE BUGS to [log in to unmask]
If this fails, mail [log in to unmask], NOT the whole list

Top of Message | Previous Page | Permalink

JiscMail Tools


RSS Feeds and Sharing


Advanced Options


Archives

March 2024
January 2024
December 2023
August 2023
March 2023
December 2022
November 2022
August 2022
May 2022
March 2022
February 2022
December 2021
November 2021
October 2021
September 2021
July 2021
June 2021
May 2021
April 2021
March 2021
February 2021
January 2021
December 2020
October 2020
September 2020
August 2020
July 2020
June 2020
May 2020
April 2020
March 2020
February 2020
January 2020
December 2019
November 2019
October 2019
September 2019
August 2019
July 2019
June 2019
May 2019
April 2019
March 2019
February 2019
January 2019
November 2018
October 2018
September 2018
August 2018
July 2018
June 2018
May 2018
April 2018
March 2018
February 2018
January 2018
December 2017
November 2017
October 2017
September 2017
August 2017
July 2017
May 2017
April 2017
March 2017
February 2017
January 2017
December 2016
November 2016
October 2016
September 2016
August 2016
July 2016
June 2016
May 2016
April 2016
March 2016
February 2016
January 2016
December 2015
November 2015
October 2015
September 2015
August 2015
July 2015
June 2015
May 2015
April 2015
March 2015
February 2015
January 2015
December 2014
November 2014
October 2014
September 2014
August 2014
July 2014
June 2014
May 2014
April 2014
March 2014
February 2014
January 2014
December 2013
November 2013
October 2013
September 2013
August 2013
July 2013
June 2013
May 2013
April 2013
March 2013
February 2013
January 2013
December 2012
November 2012
October 2012
September 2012
August 2012
July 2012
June 2012
May 2012
April 2012
March 2012
February 2012
January 2012
December 2011
November 2011
October 2011
September 2011
August 2011
July 2011
June 2011
May 2011
April 2011
March 2011
February 2011
January 2011
December 2010
November 2010
October 2010
September 2010
August 2010
July 2010
June 2010
May 2010
April 2010
March 2010
February 2010
January 2010
December 2009
November 2009
October 2009
September 2009
August 2009
July 2009
June 2009
May 2009
April 2009
March 2009
February 2009
January 2009
December 2008
November 2008
October 2008
September 2008
August 2008
July 2008
June 2008
May 2008
April 2008
March 2008
February 2008
January 2008
December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007
2006
2005
2004
2003
2002
2001
2000
1999
1998


JiscMail is a Jisc service.

View our service policies at https://www.jiscmail.ac.uk/policyandsecurity/ and Jisc's privacy policy at https://www.jisc.ac.uk/website/privacy-notice

For help and support help@jisc.ac.uk

Secured by F-Secure Anti-Virus CataList Email List Search Powered by the LISTSERV Email List Manager