CMP with 3 choice dimensions and sample selection

[Ganesh AR]

I am trying to build a joint model with sample selection and found out that STATA's CMP command does a good job of this.
I have three choice dimensions A (1,0: Binary response), B(1, 0: Binary response) and C(1,2,3,4: Ordered response).
The three independent models are:
1. Binary probit for choice dimension A ; sample size = 800
2. Binary probit for choice dimension B ; sample size = 800
3. Ordered probit for choice dimension C conditional on dimension A = 1 (Due to sample selection) ; sample size = 300

My error structure for joint model is:
I suspect there is correlation of unobserved error terms between dimension A and B
I also want to test for sample selection on dimension C conditional on dimension A = 1

I built the complete model in STATA using CMP based on the following command and obtained the results

CMP (A = Xa1 Xa2) (B = Xb1 Xb2) (C = Xc1 Xc2), indicators($cmp_probit $cmp_probit A*$cmp_oprobit)

In doing so, Stata gives me three error terms. rho_12, rho_13, rho_23

I know that rho_12 is the error between A with sample size 800 and sample size 800, rho_13 = selectivity between dimension A with sample of 800 and C with sample of 300.
What does rho_23 signify or indicate? How are the dimensions B and C linked ?

Also, is there a way to constrain the rho_23 to zero and run the same CMP models?

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a quick answer by following the FAQ on asking questions.

I suspect you have three covariances - 1 and 2 1 and 3 and 2 and 3.

[Ganesh AR]

Thank you Phil Bromiley for the suggestion.

Regarding the covariances, I would like to know if the correlation of error term between 2 and 3 is for 300 observations since 2 contains 800 observations while 3 contains only 300 observations (due to sample selection)