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Re: st: MLE est. linear form with two sets of parameters

From   Maarten buis <>
Subject   Re: st: MLE est. linear form with two sets of parameters
Date   Mon, 31 May 2010 00:52:59 -0700 (PDT)

--- On Sun, 30/5/10, Denis Kalugin wrote:
> The goal is to estimate two latent variables, let's say L1
> and L2. The variables are linked to variable y in the following
> manner:
> y=0 if L1<z<L2
> y=-1 if z>L2
> y=1 if z<L1
> L1=exp(x*b1+error)/(1+exp(x*b1+error)
> L2=min[exp(x*b1+error)/(1+exp(x*b1+error)
> , exp(x*b2+error)/(1+exp(x*b2+error)
> This is estimated via slightly altered probit (as far as I
> understand).
> P(y=-1)=norm[(log(z/(1-z)) - xb1)/sigma(error1)]
> P(y=1)=(1-norm[(log(z/(1-z)) -
> xb1)/sigma(error1)])*(1-norm[(log(z/(1-z)) -
> xb2)/sigma(error2)])
> P(y=0)=1-p(y=-1)-p(y=1)
> However, my problem right now is how to feed TWO sets of
> parameters (b1 and b2) to be estimated. If i write this
> as a linear form, then stata would generate only one 
> vector. 

Looks like your are mixing up logits and probits, either use -normal- or
use exp(.)/(1+exp(.)). The latter can be coded more briefly as 
-invlogit()- . Also note that coding normal(-xb) or invlogit(-xb) is much
more stable than (1-normal(xb)) or (1-invlogit(xb)).

Anyhow, for your immediate question: 

Your claim about how -lf- works is not correct. You really need to get 
your hands on: William Gould, Jeffrey Pitblado, William Sribney (2006) 
"Maximum Likelihood Estimation with Stata, 3rd Edition", College 
Station, TX: Stata Press.

Your model looks very similar to -zoib-, so you can type -ssc install
zoib- and look at that program. 

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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