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Re: st: Iteratively re-weighted least squares (IRLS)


From   Clive Nicholas <[email protected]>
To   [email protected]
Subject   Re: st: Iteratively re-weighted least squares (IRLS)
Date   Fri, 6 Apr 2007 21:01:46 +0000 (GMT)

Richard Sperling wrote:

I would like to use Stata (9.2 SE) to estimate the following  
inherently non-linear function by IRLS:

C = (a + b*X^g)*e,

where e is multiplicatively normal with mean 1 and standard deviation  
0.15. I cannot use -nl- to estimate this function because it assumes  
that the error term enters additively. One suggestion I have received  
is to take logs of both sides:

ln(C) = ln(a+b*X^g) + ln(e).

Is there an alternative way of estimating this equation?

----------------------------------------------------------------------------------------------------

I'm not sure if this gives you exactly what you want, and I don't know 
your data, but how about this for a kick-off?

. webuse productivity

. g u= unemp/100

. g p= private/100

. glm u p, family(bin) link(logit) irls
note: u has non-integer values

Iteration 1:   deviance =  31.93819
Iteration 2:   deviance =  7.123891
Iteration 3:   deviance =  6.021709
Iteration 4:   deviance =  6.017625
Iteration 5:   deviance =  6.017625

Generalized linear models                          No. of obs      =       816
Optimization     : MQL Fisher scoring              Residual df     =       814
                   (IRLS EIM)                      Scale parameter =         1
Deviance         =  6.017625175                    (1/df) Deviance =  .0073927
Pearson          =  6.276553692                    (1/df) Pearson  =  .0077108

Variance function: V(u) = u*(1-u/1)                [Binomial]
Link function    : g(u) = ln(u/(1-u))              [Logit]

                                                   BIC             = -5451.376

------------------------------------------------------------------------------
             |                 EIM
           u |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           p |   8.259563   15.30022     0.54   0.589    -21.72832    38.24745
       _cons |  -3.524154   1.631067    -2.16   0.031    -6.720987   -.3273207
------------------------------------------------------------------------------

Clive Nicholas





		
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