topic Re: Interpretation of RESTRICT output and LR test in Statistical Procedures

Interpretation of RESTRICT output and LR test

liu6200 — Mon, 07 Feb 2022 06:52:32 GMT

Hi SAS Community,

I used PROC MODEL to do some demand estimation with ITSUR. Inside the PROC MODEL procedure, I used RESTRICT to impose a few restrictions on the parameters. Then in the results, at the bottom of the table 'Nonlinear ITSUR Parameter Estimates', SAS printed out the estimate, std err, t value, and p value for each of the restrictions (see pic). How should I interpret these results? Does p<.0001 mean that it's valid to impose this restriction?

My second question is, in addition to these restrictions I have imposed, I would like to test another set of restrictions. Let's call them RES2. I'd like to run the ITSUR with and without RES2, then run a Likelihood Ratio Test. Could someone give some guidance on how to do that?

Thanks very much!

Angelica

Re: Interpretation of RESTRICT output and LR test

ballardw — Mon, 07 Feb 2022 16:51:27 GMT

To get a good answer to any of the questions you should include all of the code used in Proc Model.

Interpretation does depend on options used in the code.

Re: Interpretation of RESTRICT output and LR test

liu6200 — Mon, 07 Feb 2022 18:19:33 GMT

Thank you for your reply!

Below is the code in PROC MODEL. The background of this project is that I'm estimating a non-linear demand system for six products: cb, ob, cj, oj, cs, os.

proc model data=df;

	restrict gcb_cb + gcb_ob + gcb_cj + gcb_oj + gcb_cs + gcb_os = 0,
		 gcb_ob + gob_ob + gob_cj + gob_oj + gob_cs + gob_os = 0,
		 gcb_cj + gob_cj + gcj_cj + gcj_oj + gcj_cs + gcj_os = 0,
		 gcb_oj + gob_oj + gcj_oj + goj_oj + goj_cs + goj_os = 0,
		 gcb_cs + gob_cs + gcj_cs + goj_cs + gcs_cs + gcs_os = 0,
		 gcb_os + gob_os + gcj_os + goj_os + gcs_os + gcs_cs = 0,
		 acb + aob + acj + aoj + acs + aos = 1;

	lp = acb*lcb + aob*lob + acj*lcj + aoj*loj + acs*lcs + aos*los + .5*(
	gcb_cb*lcb*lcb + gcb_ob*lcb*lob + gcb_cj*lcb*lcj + gcb_oj*lcb*loj + gcb_cs*lcb*lcs + gcb_os*lcb*los +
	gcb_ob*lob*lcb + gob_ob*lob*lob + gob_cj*lob*lcj + gob_oj*lob*loj + gob_cs*lob*lcs + gob_os*lob*los +
	gcb_cj*lcj*lcb + gob_cj*lcj*lob + gcj_cj*lcj*lcj + gcj_oj*lcj*loj + gcj_cs*lcj*lcs + gcj_os*lcj*los +
	gcb_oj*loj*lcb + gob_oj*loj*lob + gcj_oj*loj*lcj + goj_oj*loj*loj + goj_cs*loj*lcs + goj_os*loj*los +
	gcb_cs*lcs*lcb + gob_cs*lcs*lob + gcj_cs*lcs*lcj + goj_cs*lcs*loj + gcs_cs*lcs*lcs + gcs_os*lcs*los +
	gcb_os*los*lcb + gob_os*los*lob + gcj_os*los*lcj + goj_os*los*loj + gcs_os*los*lcs + gos_os*los*los);

	wcb_h = acb + gcb_cb*lcb + gcb_ob*lob + gcb_cj*lcj + gcb_oj*loj + gcb_cs*lcs + gcb_os*los + bcb*(lx-lp); 
	wob_h = aob + gcb_ob*lcb + gob_ob*lob + gob_cj*lcj + gob_oj*loj + gob_cs*lcs + gob_os*los + bob*(lx-lp); 
	wcj_h = acj + gcb_cj*lcb + gob_cj*lob + gcj_cj*lcj + gcj_oj*loj + gcj_cs*lcs + gcj_os*los + bcj*(lx-lp); 
	woj_h = aoj + gcb_oj*lcb + gob_oj*lob + gcj_oj*lcj + goj_oj*loj + goj_cs*lcs + goj_os*los + boj*(lx-lp);
	wcs_h = acs + gcb_cs*lcb + gob_cs*lob + gcj_cs*lcj + goj_cs*loj + gcs_cs*lcs + gcs_os*los + bcs*(lx-lp);

	fit wcb wob wcj woj wcs / itsur covb outest=coef converge=.00001  maxit=1000;
            parms acb bcb  gcb_cb gcb_ob gcb_cj gcb_oj gcb_cs gcb_os
		  aob bob         gob_ob gob_cj gob_oj gob_cs gob_os
		  acj bcj                gcj_cj gcj_oj gcj_cs gcj_os
		  aoj boj                       goj_oj goj_cs goj_os
		  acs bcs                              gcs_cs gcs_os
 		  aos                                         gos_os;

run;
quit;