Re: st: MLE Non-linear Program

[Partha Deb <partha.deb@hunter.cuny.edu>]

Steven,

I have a number of thoughts.

1. I'm not sure why you need to estimate your model using ML.  A simple 
transformation of your model parameters renders the model linear in 
parameters, i.e., you can write

`xb'=`a0'+ `a1'*lnwaterdist +`a2'*totindexa  ///
+ `b1'*(forestsaa+`lambda'*forest_vdc5a)+ 
`b2'*(ldistkillnov+`gamma'*ltotkill)

can easily be written as

`xb'=`a0'+ `a1'*lnwaterdist +`a2'*totindexa  ///
+ `b11'*forestsaa + `b12'*forest_vdc5a + `b21'*ldistkillnov + `b22'*ltotkill

and this can be estimated using -regress- .  Following regress, you can 
use -nlcom- to recover b1, lambda, b2 and gamma.

2. It does seem a bit odd that lambda is a logit type transformation of 
kappa, but after creating lambda2 as a logit transformation of gamma, it 
does not enter the specification.

3. An argument against what I have suggested is that your specification 
constrains lambda and lambda2 to be in (0,1) while OLS will not respect 
that.  Perhaps this is an important constraint, but if it is true, OLS 
should recover that.  Else, it might be evidence that your model is 
misspecified.

5. Why not use -lnnormalden- to specify the normal density?  You would 
be sure then, that there are no coding errors there.

6. sigma should be constrained to be positive.  The Stata-ish solution 
is to think of lnsigma as the parameter and specify sigma = exp(lnsigma).

Hope this helps.

Partha



On 11/19/2010 2:03 PM, Steven Archambault wrote:
> Hi all,
> I am running this MLE nonlinear program below. It has trouble
> converging , I guess because of the complexity of having to estimate
> kappa and gamma. Does anybody have any suggestions for improving the
> code, while still getting estimates for gamma and kappa?
> It works fine for estimating kappa only and gamma only. Thanks!
>
> capture program drop simplemle
> program simplemle
> args lnL a0 a1 a2 eta b1 b2 kappa gamma
> tempvar xb sigma lambda lambda2
> quietly gen double `lambda'=exp(`kappa')/(1+exp(`kappa'))
> quietly gen double `lambda2'=exp(`gamma')/(1+exp(`gamma'))
> quietly gen double `xb'=`a0'+ `a1'*lnwaterdist +`a2'*totindexa  ///
> + `b1'*(forestsaa+`lambda'*forest_vdc5a)+ `b2'*(ldistkillnov+`gamma'*ltotkill)
>
> quietly gen double `sigma'=exp(`eta')
> quietly replace
> `lnL'=-.5*ln(2*_pi)-.5*ln((`sigma')^2)-.5*(foodindx10-`xb')^2/(`sigma')^2
> end
> ml model lf simplemle (a0:) (a1:) (a2:) (eta:) (b1:) (kappa:) (b2:) (gamma:)
> ml init  1 1 .1 .1 .1 1 1 1 , copy
> ml maximize
>
> I get messages like: (Iteration 70:  log likelihood = -3354.8283  (not concave)
> numerical derivatives are approximate
>
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--
Partha Deb
Professor of Economics
Director of Graduate Studies
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398
http://urban.hunter.cuny.edu/~deb/

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	- Bob Marley

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