07-27-2013 02:53 PM
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.
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;
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.