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How to estimate simultaneously two or plus variables?

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How to estimate simultaneously two or plus variables?

Hi all,

I have to estimate the following model:

Model specification.jpg

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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Posts: 2,655

Re: How to estimate simultaneously two or plus variables?

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

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