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07-27-2013 02:53 PM

Hi all,

I have to estimate the following model:

How can I estimate simultaneously the three coefficients (delta, beta1 and beta2)? In this way, I am able to obtain an unique coefficient for all three variables.

I try to find any functions in PROC MODEL, but I don't get it.

Any suggestions?

Thanks,

Gabriele

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Posted in reply to Gds88

07-29-2013 01:46 PM

This may seem naive, but it looks like there are 5 parameters to estimate, with three independent variables and one dependent variable. Additionally, it appears, based on the subscripting, that this is a time series (indexing on t). If you can assume independence (not likely), then PROC NLIN will enable you to fit the equation. Something like:

proc nlin data=a;

parms lambda= delta= beta_0= beta_1= beta_2=;/* Provide starting values for each of the parameters */;

exponent=beta_0 + beta_1*X1 + beta_2*X2;

s = lambda * delta * P ** exponent;

output out=b predicted=yp;

run;

See if this works. It does require multiple observations, probably at least 40, to get a decent fit. Notice also that no matter what you do, lambda and delta will be completely confounded--only their product can be fit, unless there is some other constraint on one or the other.

Steve Denham