# st: maximum likelihood estimation of nonlinear models

 From "Paulo Regis" <[email protected]> To <[email protected]> Subject st: maximum likelihood estimation of nonlinear models Date Sun, 24 Jul 2005 19:22:01 +0100

hi all,

I am working with nonlienar least squares (nl) and maximum likelihood (ml) estimators since I have a nonlinear specification. My problem is I cannot find the appropiate notation for my log likelihood function. My dependent variable (y) has a normal distribution. the model is:

y=x1^b1*x2^b2*x3^b3+e

I checked "Maximum Likelihood Estimation with Stata" (gould and Sribney). In page 45, they present the programme to estimate:

y=b0+b1*x1+b2*x2+b3*x3^b4

which is:

program define linreg
version 8.0
args lnf theta1 theta2 theta3 theta4
quietly replace `lnf'= ln(normd((\$ML_y1-`theta1'-
`theta2'*x3^`theta3')/`theta4'))-ln(`theta4')
end
ml model lf linreg (y = x1 x2) /beta3 /beta4 /sigma
ml maximize

So, i tried something similar

program define linreg
version 8.0
args lnf theta1 theta2 theta3 theta4
quietly replace `lnf'= ln(normd((\$ML_y1-x1^`theta1'
*x2^`theta2'*x3^`theta3')/`theta4'))-ln(`theta4')
end
ml model lf linreg (y=) /beta1 /beta2 /beta3 /sigma
ml maximize

but it did not work. I am not sure if the problem is my notation for the log likelihood function in the programme in lines 4-5 or the "ml model" statement in line 7.
I would appretiate any suggestion.

Cheers - Paulo

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