Hi,
I am dealing with 3 highly correlated binary traits, and would like to
analyze them jointly with a trivariate probit model. I am using the
approach described by Albert and Chib that a latent variable 'lambda' is
augmented for each binary outcome as
lambda = X beta + e
here e is a vector of [e1, e2, e3]'
and assuming that e ~ N(0, R)
In most literature, the residual variances were all fixed at 1, so R is
equal to a correlation matrix.
My question is, do I have to fix all the residual variances to one? Can I
fix the first residual variance to 1 and estimate the others? I am using
a Bayesian approach, so is it OK that I assume a scaled inverse Wishart
prior on R[2:3, 2:3]?
Any suggestions and comments are appreciated.
Yu-mei Chang
Computational Geneticist
Department of Dairy Science
University of Wisconsin, Madison
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