[Limdep Nlogit List] ML and System ML with Ordered Probit

[William Greene]

David.  Here is an adaptation of what you are trying to do, with a
particular data set (the health care data on the website for my text)
and a particular formulation of the regression and ordered probit 
model. You should be able to adapt it to your specific problem.
Regards,
Bill Greene

reje;year # 1988 $
create ; y = newhsat $
recode ; y ; 0/4=1 ; 5/7=2 ; 8/10=3$
create ; y = y - 1 $
hist;rhs=y$
name ; x = one,educ,married,hhkids $ $
create ; h = hhninc $
name ; z=one,age,educ$
regr;lhs=h;rhs=z $
matrix ; a0 = b $
calc   ; s0 = s $
orde  ; lhs = y ; rhs = x $
matrix ; b0=b;mu0=mu$
calc   ; r0=0 $
crea    ; y0=y=0 ; y1=y=1 ; y2=y=2 $
maximize 
;start = beta0,mu0,a0,s0,r0
;labels= beta1,beta2,beta3,beta4,mu1,a1,a2,a3,sgma,rhoeu
;fcn   = eps = h - a1'z |
         dr = 1/sqr(1 - rhoeu*rhoeu) |
         index = dr*(beta1'x - rhoeu/sgma*eps) |
         p0 =     phi(       - index)      |
         p1 =     phi(mu1*dr - index) - p0 |
         p2 = 1 - phi(mu1*dr - index)      |
         log(y0*p0 + y1*p1 + y2*p2) 
         + log(n01(eps/sgma)/sgma)
         ; maxit=10 ; output=3  $
         ; fix=rhoeu $






----- Original Message -----
From: "David Tufte" <tufte at suu.edu>
To: limdep at limdep.itls.usyd.edu.au
Sent: Friday, May 7, 2010 4:07:06 PM GMT -05:00 Colombia
Subject: [Limdep Nlogit List] ML and System ML with Ordered Probit

It has been a month, but I've been researching my problem. Sorry for the delay.

I want to do a system ML where 1 equation is an ordered probit, and the other is a standard regression. The latter will generate a variable that goes into the former, so the cross-equation restrictions are important for efficiency.

I read what Bill wrote, and the material on pg. 815 is straightforward. But it isn't what I need.

The hole in what I need to know is how to code an ML function into LimDep and then maximize it. What I could really use is an example of an ordered probit (or something similar), done from scratch with FIML, so that I could compare it to the result from the ORDERED command's output. I am most concerned about making sure that I have set up the identification properly in my ML routine so that I can duplicate what ORDERED produces. I think if I had that, then combining it with another regression into a system with cross-equation constraints would be easy.

Does anyone have an example code and dataset like this?

Regards,
Dave Tufte
School of Business
Southern Utah University

I copied my original post and Bill Greene's reply below. 
==========================================

David. In Section 23.7 of the 6th edition of my text, you will
see how to do this for a binary probit model with an endogenous
continuous variable. It's fairly simple - indeed, that one is
actually built into limdep.  For an ordered probit model, you
will need to modify the second part of the log likelihood. It's
going to be a little involved, but doable.  As a first step, if 
you convert your ordered probit dependent variable to 0 or >0,
you can use this routine directly. It will at least give you an
idea where you are going.

==========================================

A referee believes this will make a difference in my results.

I have a 2 equation system. I estimated one equation by OLS, obtained 
generated regressors from it, and used them in variables in an 
ordered probit. This method is inefficient due to multiple causes of 
non-spherical errors - but it was convenient to do it this way with 
simple LimDep commands straight out of the manual.

It seems best, given the referee's complaint, to follow McAleer and 
McKenzie and estimate this system by FIML to solve all of the 
non-spherical error issues at once.

I know how to set up and maximize the likelihood function of a 
simpler system in RATS (where my coding skills are better), but to do 
this I would have to figure out how to modify the likelihood for an 
ordered probit.

I am wondering if anyone can point me towards 1) a program or example 
of how to set up and estimate a system of equations by FIML in 
LimDep, and 2) a program showing the ordered probit likelihood in 
LimDep that I could modify and paste into that.

David Tufte
Associate Professor
Department of Economics and Finance
School of Business
Southern Utah University
351 W. University Blvd.
Cedar City  UT  84720
351 W. University Blvd.
Cedar City  UT  847820


351 West Center St.
Cedar City, UT 84720

Office: (435) 586-5407
Fax:     (435) 586-5493 

http://www.suu.edu/faculty/tufte


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