ordinal probit regression–latent trait approach multivariate data?

Hello, all.

I am in dire need of some help. I am trying to run a multivariate (multiple, non-independent response variables) ordered probit regression model. I’ve had success with univariate models using both “polr(method=’probit’)” and “vglm(cumulative(link=’probit’))” functions from the MASS and VGAM packages, respectively. Thomas Yee, who maintains the VGAM package, communicated to me that “vglm” couldn’t be used for the multivariate model. So, back to square one.

In the univariate setting, I’ve treated the ordinal response variable as a latent trait, modeled with standard normal distribution (e.g., Johnson and Albert, 1999:127-130). What I’d like to do is include an additional, ordinal response variable, so that the two (non-independent) response variables are treated as latent traits and modeled with a standard bivariate normal distribution. Any suggestions are welcome, and I can post a link to a sample of the data, if that helps. Thanks.

–Trey

Johnson VE and JH Albert. 1999. Ordinal Data Modeling. New York: Springer-Verlag.