Generalised residuals after ordered probit

[Ujjwal]

Dear all,

I am trying to estimate a 2SRI model with two endogenous variables, one binary and the other is a five point ordinal. This will have two first stage estimations, one through probit and the other through ordered probit. Therefore, I need to calculate residuals after probit and ordered probit regressions. I am particularly struggling to find any solution for ordered probit residuals.

https://www.statalist.org/forums/for...of-2sri-method

In the above thread, Jeff Wooldridge suggested a generalised residuals for ordered probit (Vella, 1993). But that was from January 2017. I was wondering if anyone has implemented that with Stata by now.

Thanks in advance.

Ujjwal Kumar Das
3rd Year, PhD Student, Economics
University of Leeds, UK

[Tom Kisters]

Dear Ujjwal,

Have you ever been able to find a solution for this?

Kind Regards,

Tom Kisters

[FernandoRios]

Hi Tom
For the case of a simple order probit, you can get the generalized residuals using the score option:

clear
set obs 10000
gen x=rnormal()
gen e=rnormal()
gen y = 1 + x+ e

*xtile qy=y, n(10)

gen qy=ceil(y/1)
replace qy=6  if  qy>6
replace qy=-3 if  qy<-3

oprobit qy x
predict ger , score
scatter ger e e

Unfortunately, the GER for the panel version (xtoprobit) is more complicated.
HTH

[Tom Kisters]

FernandoRios Thank you very much for your answer! Ian Bowen just pointed this out to me last night as well (https://www.statalist.org/forums/for...ith-panel-data).

Is there any chance you know anything about the inner workings of the residual? More specifically what the value of pie (the estimated density at point ji refers to (see the fragment below describing the residual in Vella (1993)?

Vella, F. (1993). A Simple Estimator for Simultaneous Models with Censored Endogenous Regressors. International Economic Review, 34(2), 441-457. doi:10.2307/2526924

[FernandoRios]

not sure what your question is. As it says in the next PI_ij is the probability of observation i belonging to group j.
you would get this using something like,

predict pr*, pr

[Tom Kisters]

FernandoRios Sorry, I have should have been clearer. You seem to be referring to the capital letter PI_ji, but there is also the small pi_ji, which is "the estimated value of the density at that point". This is the part that is unclear to me (and also to some others going on questions on this forum). What is the estimated value of the density at point ji?

[FernandoRios]

Look at equation 3 in this paper
https://journals.sagepub.com/doi/pdf...867X0700700202

the numerator is equivalent to the pi_ij, whereas the denominator is PI_ij

[Tom Kisters]

FernandoRios

Okay, I am really doing my best to understand:

So that means that the denominator is equal to the predicted probability for each category.
And that predicted probability is: the deviation from the mean of the prediction (?) for category j, minus the deviation from the mean of the prediction (?) for category j + 1.
And the the estimated value of the density at that point (capital pi, the denominator), is the just the opposite (the deviation from the mean of the prediction (?) for category j + 1, minus the mean of the prediction (?) for category j) ?

[Himanshu Arha]

Hi Tom
For the case of a simple order probit, you can get the generalized residuals using the score option:

clear
set obs 10000
gen x=rnormal()
gen e=rnormal()
gen y = 1 + x+ e

*xtile qy=y, n(10)

gen qy=ceil(y/1)
replace qy=6 if qy>6
replace qy=-3 if qy<-3

oprobit qy x
predict ger , score
scatter ger e e

Unfortunately, the GER for the panel version (xtoprobit) is more complicated.
HTH

Hi FernandoRios

I am struggling with a similar problem, where I am using 2 stage residual inclusion to correct for endogeneity in my model. However, for first stage, I am using Poisson Regression. Can we generate the generalized residuals in this case also? Can you also please guide me with STATA command for this?