## Programming the statistical procedures from SAS

Occasional Contributor
Posts: 18

Hi,

I am carrying out a non-linear model with NLMIXED and I am aware that it finds the parameter estimates which maximise the likelihood fn. But what is the likelihood function? I have assumed the residuals are normally distributed, and the code is:

proc nlmixed;

parms

ED50  5 to 250 by 5

Emax  -2 to -1  by 0.1

V     0.1

BETA0 1

s 1;

pred = (x* (Beta0)) +  (y**s * Emax) / ( y**s + ED50**s );

model R ~ normal( pred, V);

Where R is the response, x and y are explanatory variables.

So I believe I'm modelling R= (x* (Beta0)) +  (y**s * Emax) / ( y**s + ED50**s )  and the errors are normal with the variance V.

Proc NLMIXED finds the parameters that maximise the likelihood fn, so what is this function?

Is it

where mu=(x* (Beta0)) +  (y**s * Emax) / ( y**s + ED50**s )   and sigma^2=V?

IE the ML fn for the normal dist, with the model as mu?

xxx;

Posts: 2,655

The simple answer is YES.  That is the likelihood function with all of the definitions you present.  Check the SAS-L archives for posts on NLMIXED by David Cassell, Dale McLerran and several others.  There should be code there that will deal with this as needed.

Steve Denham

SAS Super FREQ
Posts: 3,839

I wrote a brief discussion of (univariate) MLE that includes code and an example. The regression approach is similar with mu replaced by the linear predictor. You should definitely check out the discussion with formulas in the PROC GENMOD documentation.

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