how to make restriction work in PROC NLIN

[JacAder]

I am running the regression y = a + b*x, by ID, with the restriction of a=0 and b>0. 

In the PROC NLIN, the bounds statement requires inequality, so my code does not work.

1) if I simply set model = b*x (and delete a=0 in parameters and bounds statements), does that yield the result of a=0? seems like the result is desired, but I am not sure.

2) in the output dataset aa, _TYPE_ = "FINAL" are the estimated parameters, am I right?

Thank you and have a great holiday!

proc nlin data=sample outest=aa noprint;
   parameters a=0 b=1;         
   bounds  a=0, b>0;
   model y = a + b*x;
   by id;
   output out=bb  r=resid  parms=a b;
run;

[FreelanceReinh · Accepted solution]

Hi @JacAder,

---

@JacAder wrote:

Also, in the output dataset aa, _TYPE_ = "FINAL" are the estimated parameters, am I right?

---

Yes, the observation with _TYPE_="FINAL" would contain the final parameter estimates.

If parameter a is known to be zero, I would just simplify the model equation to y = b*x and not mention a anywhere in the step. Since y = b*x is a linear model (without an intercept), I would start with PROC REG or PROC GLM and use the NOINT option of the MODEL statement. If the estimated slope b is positive, the restriction is met. Otherwise, given that there are reasons to expect a positive slope, I would suspect one or more outliers to distort the estimation. I don't think that PROC NLIN with its BOUNDS statement would really help in this situation: The outliers would mislead PROC NLIN's algorithms as well and I would expect a poor model fit with an estimate of b close to zero. I'd rather investigate the suspected outliers (scatter plot, ...) and consider robust regression (PROC ROBUSTREG) to deal with them.

[JacAder]

Really appreciate your help!