proc nlmixed for custom log likelihood

Forecaster — Mon, 07 Apr 2025 14:46:15 GMT

hello, I'm trying to code up the likelihood below using Proc NLMIXED.

I have dataset that is person period, sorted by id and time. here is the structure of dataset, sorted by ID and time.

ID	Time	y (Event)	last_ob	x1
1	1	0	1	20
2	1	0	0	21
2	2	0	1	20
2	3	0	0	10
2	4	1	1	5
3	1	0	0	12
3	2	0	0	23
3	3	0	0	10
3	4	0	0	4
3	5	0	0	23
3	6	0	0	10
3	7	0	1	5

Below is the sas proc NLMIXED code:

proc nlmixed data=your_data qpoints=50;
   parms mu=0 sigma2=1 beta1=0;
   bounds sigma2 > 0;

   /* Linear predictor */
   linpred = eta + beta1*x1;
   theta = exp(linpred) / (1 + exp(linpred));
   log_surv = log(1 - theta);

   /* Accumulate log survival up to time t-1 using ZLAG */
   if time = 1 then acc_log_surv = 0;
   else acc_log_surv = ZLAG(acc_log_surv) + ZLAG(log_surv);

   /* Event or censoring contribution */
   if y = 1 then loglik = acc_log_surv + log(theta);
   else if last_obs = 1 then loglik = acc_log_surv + log(1 - theta);
   else loglik = .;

   model y ~ general(loglik);
   random eta ~ normal(mu, sigma2) subject=id;
run;

I have two part question,

what would "y" in model general(loglik) be? and also how do I code up cumulative product (or log sum) of P(T) and S(T) since retain and first.id is not available. I just used zlag based on time = 1? is this correct?

Any help would be greatly appreciated.

Thanks

Sri

Re: proc nlmixed for custom log likelihood

Season — Tue, 08 Apr 2025 09:32:11 GMT

I am not an expert in compiling codes for maximizing custom likelihoods, but I know somebody is. There is a monograph dedicated to the theory of maximum likelihood estimation as well as how to implement it in statistical softwares including SAS named Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB (Statistics in Practice Book 112) 1, Millar, Russell B. - Amazon.com. Issues on maximizing custom likelihoods via SAS procedures like PROC NLMIXED and PROC NLP are discussed frequently in that book. While waiting for an expert in the community for his/her help, you may also consult the book to see if there is anything useful. In addition, writing an e-mail to the author of the book to directly raise your question to him/her might be of help.

topic proc nlmixed for custom log likelihood in Statistical Procedures

proc nlmixed for custom log likelihood

Re: proc nlmixed for custom log likelihood