multivariate ordered probit regression---use standard bivariate normal distribution?

#1
Hello.

My two previous posts (1 & 2) have about 100 views each, but no replies, so I must have done a poor job asking the question. So, here is the general question: how can I run a run a multivariate (more than one non-independent, response variables) ordered probit regression model? I've had success doing this in the univariate case using the vglm() function in the VGAM package. For example:

unvar.prob<-vglm(y~x,cumulative(link="probit",parallel=FALSE,reverse=TRUE))

This would fit a unrestricted cumulative probit model (or a "thresholds of change" model) with the ordered response variable treated as a latent trait modeled with a standard normal distribution. 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.

The VGAM package includes the function binormal(), which seems like it should be of some use here, but if so, I don't know where/how it fits into the model. I've included the results of running the model with the two response variables separately. Any suggestions are welcome, and I've attached the data file, if that helps. Thanks.

--Trey

Code:
unvar.prob1<-vglm(pube3~age,data=refdata,cumulative(link="probit",parallel=FALSE,reverse=TRUE))
> unvar.prob1
Call:
vglm(formula = pube3 ~ age, family = cumulative(link = "probit",
parallel = FALSE, reverse = TRUE), data = refdata)

Coefficients:
(Intercept):1 (Intercept):2 age:1 age:2
-1.65895567 -2.14755951 0.06688242 0.04055919

Degrees of Freedom: 1492 Total; 1488 Residual
Residual Deviance: 1188.909
Log-likelihood: -594.4543

Code:
unvar.prob2<-vglm(auric4~age,data=refdata,cumulative(link="probit",parallel=FALSE,reverse=TRUE))
> unvar.prob2
Call:
vglm(formula = auric4 ~ age, family = cumulative(link = "probit",
parallel = FALSE, reverse = TRUE), data = refdata)

Coefficients:
(Intercept):1 (Intercept):2 (Intercept):3 age:1 age:2
-2.07719235 -2.43422370 -2.99123098 0.07319632 0.05133132
age:3
0.03797696

Degrees of Freedom: 2238 Total; 2232 Residual
Residual Deviance: 1583.47
Log-likelihood: -791.7348

*************
Trey Batey--Anthropology Instructor
Division of Social Sciences
Mt. Hood Community College
Gresham, OR 97030
 

Dason

Ambassador to the humans
#2
Re: multivariate ordered probit regression---use standard bivariate normal distributi

Wish I could help - I'm not too well versed in many multivariate methods though and a multivariate ordered probit isn't something I've had the pleasure to attempt to do.
 
#3
Re: multivariate ordered probit regression---use standard bivariate normal distributi

Hi, Dason.

I appreciate your taking the time to reply. It's no big thing, if you can't help; it's not seeing any replies that is a killer! Hopefully, someone will come across the original post and have some suggestions. Thanks, again.

--Trey