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Re: st: NLLS w/ normal distribution - some parameters not estimated

From   Maarten buis <>
Subject   Re: st: NLLS w/ normal distribution - some parameters not estimated
Date   Sun, 13 Jun 2010 17:29:34 +0000 (GMT)

--- On Sun, 13/6/10, Denis Kalugin wrote:
> I'm trying to do a non-linear least squares estimation to
> nail down a latent dependence. The latent variables can be
> regressed on a linear form and look like
> L1=xb1+error1
> L2=xb2+error2
> The probabilities of observing a value of y is given by
> P(y=-1)=P(L1<z)=norm( (z-xb1)/error1 ),
> P(y=1)=P(z<min(L1,L2))=( 1- norm( (z-xb1)/error1 ) )*(
> 1- norm( (z-xb2)/error2 ) )
> P(y=0) = 1 - P(y=1) - P(y=-1)

This doesn't sound like a problem for -nl-, rather a problem
for -ml- (or maybe -gmm-). Basically, -nl- still assumes that
the dependent variable is continuous, which is not the case
in your problem. Also note that the variances of the error
terms are probably not identified. Finally, do you think that
these error terms are uncorrelated? 

Hope this helps,

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


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