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?
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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
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Clive Nicholas
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