04-12-2014 06:31 AM
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:
ED50 5 to 250 by 5
Emax -2 to -1 by 0.1
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?
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?
Please help, I am very confused
04-14-2014 11:05 AM
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.
04-16-2014 08:45 AM
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.