topic Re: Proc NLP, choice of covariance matrix & confidence interval in Mathematical Optimization, Discrete-Event Simulation, and OR

Proc NLP, choice of covariance matrix & confidence interval

gp4 — Thu, 22 Feb 2024 17:10:09 GMT

I am using proc nlp for a fairly simple minimization problem. Only two parameters are being estimated, the sample size is < 40 so I accept the SAS default NRRIDG optimization. However, I am unsure how one makes the best choice for approximate covariance matrix of the parameters, & the choice between Wald and Profile confidence intervals.

I ran the problem with each of the six covariance matrix options. There are some substantial differences in the standard errors for the methods. Also, 2 of the 6 covariance methods do not produce profile confidence intervals. My question is, other than just running all combinations and picking the one that gives the smallest SE or narrowest confidence interval, is there guidance on how one chooses these settings?

Re: Proc NLP, choice of covariance matrix & confidence interval

RobPratt — Thu, 22 Feb 2024 21:40:25 GMT

I don't have a recommendation about when to use which COV= formula, but I want to point out that PROC NLP is a legacy procedure that was last documented in SAS/OR 14.1 (released in 2015). That doc has a section on Covariance:

Covariance Matrix :: SAS/OR(R) 14.1 User's Guide: Mathematical Programming Legacy Procedures

It also has an example:

Example 6.6 Maximum Likelihood Weibull Estimation :: SAS/OR(R) 14.1 User's Guide: Mathematical Programming Legacy Procedures

PROC NLP users are encouraged to instead use the NLP solver in PROC OPTMODEL.

The corresponding documentation links are:

SAS Help Center: Covariance Matrix

SAS Help Center: Maximum Likelihood Weibull Estimation

The PROC NLP doc also has a section about migrating to PROC OPTMODEL:

Rewriting NLP Models for PROC OPTMODEL :: SAS/OR(R) 14.1 User's Guide: Mathematical Programming Legacy Procedures

Re: Proc NLP, choice of covariance matrix & confidence interval

gp4 — Thu, 22 Feb 2024 22:11:53 GMT

I have been thru the documentation. It may be a deficit in my knowledge, but seeing the definitions of the covariance estimators doesn't suggest much too me in terms of useful information. I opted for one of the simpler ones, as the problem isn't big. As for NLP v OPTMODEL, NLP is working and is so much less messy than OPTMODEL, that I'll stick with it for this project.