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AW: st: Trivariate ordered probit model in Stata?


From   "Karabulut, Yigitcan" <karabulut@finance.uni-frankfurt.de>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   AW: st: Trivariate ordered probit model in Stata?
Date   Tue, 4 Jan 2011 17:06:32 +0100

Thank you for the prompt response and helpful comment, Stas.

The full explanation of the system is as below - Variables with stars denote the continuous versions of the latent variables without stars:

y1*=X*beta1+epsilon1
y2*=X*beta2+gamma*y1*+epsilon2
y3*=X*beta3+theta1*y1*+epsilon3

where

Y1 = 1 if y1* < c11
     2 if c11<y1*<12
     3 if c12 < y1*

Y2 = 1 if y2* < c21
     2 if c21<y2*<22
     3 if c22 < y2*

Y3 = 1 if y3* < c31
     2 if c31<y3*<32
     3 if c32 < y3*

Without Y3; it is the same model as explained in Stata journal paper by Zurab Sajaia (page 2, equations 1-3) (for reference and link, please see below). 

I believe that the model above deviates from trivariate ordered probit model in the sense that Y2 and Y3 are seemingly unrelated. However, -Y1 and Y2- and -Y1 and Y3- are not seemingly unrelated and for these cases full maximum likelihood has to be employed.

Reference:

Sajaia, Zurab; "Maximum likelihood estimation of a bivariate ordered probit model: implementation and Monte Carlo simulations", Stata Journal.

http://www.adeptanalytics.org/download/ado/bioprobit/bioprobit.pdf

Yigitcan Karabulut

Research Assistant
Chair of Finance, Retail Banking Competence Center (RBCC), Goethe University Frankfurt

House of Finance
Grüneburgplatz 1
60323 Frankfurt
Phone: +49 (0) 69 798 33859
Mobile: +49 (0) 178 68 29 223
E-mail: karabulut@finance.uni-frankfurt.de
www.finance.uni-frankfurt.de
________________________________________
Von: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] im Auftrag von Stas Kolenikov [skolenik@gmail.com]
Gesendet: Dienstag, 4. Januar 2011 16:17
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: Trivariate ordered probit model in Stata?

On Tue, Jan 4, 2011 at 8:03 AM, Karabulut, Yigitcan
<karabulut@finance.uni-frankfurt.de> wrote:
> I have a question regarding the feasibility of a trivariate ordered probit model in Stata 11: I would like to estimate a trivariate probit model where Y1,Y2 and Y3 are ordered variables all of which take the values 1 &  2 & 3:
>
> Y1=X*beta1+epsilon1
> Y2=X*beta2+gamma*Y1hat+epsilon2
> Y3=X*beta3+theta1*Y1hat +epsilon3
>
> However, while constructing the variance covariance matrix, I would like to allow correlation just for -Y1 and Y2- and -Y1 and Y3-. There is no correlation between Y2 and Y3. Therefore, I assume the relation between Y2 and Y3 is seemingly unrelated.

To clarify: is it really the predicted value of Y1 that goes into the
regression for Y2? Or do you mean the continuous analogue of Y1
(typically denoted by a star in econometric textbooks)?

And another clarification: you already have Y1 or Y1hat in the
regressions for Y2 and Y3; do you mean there's some unexplained
correlation left in epsilons?

Have you established identification of this system if all variables
were continuous, with the restrictions you impose? If it is not
identified, then there is no way the ordered version of it will be
identified.

> Do you think whether it makes sense to estimate two seperate bivariate ordered probit models and combine them using the command suest, i.e.:
>
> bioprobit Y1 Y2 X, vce(cluster id)
> estimates store p1
> bioprobit Y1 Y3 X, vce(cluster id)
> estimates store p2
> suest p1 p2

It might work. Better yet, I would try two or three different
approaches and see if they give the same results. -cmp- is the first
thing that jumps to my head when I see stuff like this; -gllamm- is
the second thing.


--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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