How to include offset parameters in NLMIXED

[SBS]

Could anyone help me on how to include offset parameter in NLMIXED model with negative binomial? Is the below inclusion of log_TotalWordsInSentence  (log of number of words in a sentence) variable correct?

proc nlmixed data=myData;
xb = b0 + b1a*(Gender = 'female') + u;
mu = exp(xb + log_TotalWordsInSentence);
m = 1/alpha;
ll = lgamma(CountPronounsInSentence+m)-lgamma(CountPronounsInSentence+1)-lgamma(m)
+ CountPronounsInSentence*log(alpha*mu)-(CountPronounsInSentence+m)*log(1+alpha*mu);
model CountPronounsInSentence ~ general(ll);
random u ~ normal(0,s2u) subject=person_id;
run;

[Rick_SAS]

@pau13rown is probably a better person to answer this, but your formula looks okay to me. Alternatively, instead of 

mu = exp(xb + log_TotalWordsInSentence);

you could use

mu = TotalWordsInSentence*(exp(xb));

which is equivalent (take log of both sides, bring  log_TotalWordsInSentence to the left, combine logs, then exponentiate.)

[SBS]

Thanks a lot Rick. I hope Paul Brown responds.

[pau13rown · Accepted solution]

sorry, i dont visit the message boards as frequently as i'd like to.... The code looks ok to me. Personally for clarity i might write it as:

bounds b2<=1, b2>=1;

xb = b0 + b1a*(Gender = 'female') + b2*log_TotalWordsInSentence + u;
mu = exp(xb);

and a minor thing: I'd reduce the length of the variable name 'CountPronounsInSentence' to make it readable, i didn't bother to read the loglikelihood equation ("ll = ")... because it's hard to read

[SBS]

Thanks a to Paul!