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RE: st: RE: nonlinear regression using GMM


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: nonlinear regression using GMM
Date   Wed, 2 Jan 2013 08:57:16 -0600

Jay - Since Usman didn't specify the complete model, I was assuming E(Y|x) = g(x, b) + u = L(x,c) + u, where L(x,b') is linear in my transformed parameters (b'). Doesn't your comment apply more to transforming the dependent variable to achieve "linearity"? 


y|x = exp(x'b) + u doesn't mean log(y|x) can be written log(y|x) = x'b' + u' where u' is an additive error term.

Al F.



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of JVerkuilen (Gmail)
Sent: Wednesday, January 02, 2013 8:43 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: nonlinear regression using GMM

On Wed, Jan 2, 2013 at 9:30 AM, Feiveson, Alan H. (JSC-SK311) <alan.h.feiveson@nasa.gov> wrote:
> Usman -I assume what you have written is the right-hand side of E(Y|DP, lr1, etc.) where Y is your dependent variable. If so, this looks linear to me if you re-parameterize as follows:
>
>
> E(Y'|lr1, DP, etc.) = A0*w1*DP + A1*DP*lr1 + A2*DP*w2 + A3*DP*w3 + 
> A4*DP*y1 + A5*DP*y2 + A6*DP*y3
>
> where Y' = Y - lr1 and where A0 = {a0}*{a1}, A1 = {a0}, A2 = {a0}*{a2},  etc.
>
>
> Thus, you have a an equation that is linear in 7 parameters (A0, A1, 
> .., A6)

I suppose it would depend on the error process that is assumed. So if you have a fully multiplicative model the notion is that the errors are multiplicative too. If that's not what's assumed the expected value structure may be linearizable, but the error term may not. So

     E(y|x) = exp(x' b) + u

is not linearizable while

     E(y|x) = exp(x' b + u)

is. Thus I think the original poster needs to decide what the model is, not just the mean structure.
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