Two part model with (1) Probit (2) Ologit or Oprobit

[Chejen Wang]

Dear Statalist users,

I am doing a project with two part model. The first equation is a probit, and the dep_var of the second equation is ordered (hierarchical) multi-level variable. I have searched most of literature database available to me. Most of the two part model deal with (1) probit + (2) NebBin or OLS. But I did not find any paper discussing a two-part model (probit + ordered probit or logit). My question is: Can I use probit and then calculate the inverse of Mills’ ratio. Use the inverse of Mill's ratio in the second equation?

(1) equation: dep_var is 0 or 1

probit dep_var ind_vars

predict xb, xb

gen imr = normd(xb)/normprob(xb)


(2) equation: dep_var_2 is ordered

ologit dep_var_2 ind_vars imr

Is there any problem to use a model like this? Or is there any paper discussing probit + oprobit / ologit model?

Any comments is highly appreciated. Thanks.

[Phil Bromiley]

You don't explain the point of the two equations. Is this a selection model or what?
You can probably directly model this in SEM or CMP.

[Chejen Wang]

You don't explain the point of the two equations. Is this a selection model or what?
You can probably directly model this in SEM or CMP.

Dear Phil,

Thanks for your reply.
Yes, it is selection model. As my data is about medical service, there are a lot of zero observations. The theory goes like that a patient's first visit his doctor comes from the patient's own decision. After the first time, the frequency of the patient's medical demand might be affected by his doctor's decision. So, there is no recursive or simultaneous structure in theory. Do you think SEM and CMP are good choices?

with best regards,

Chejen