PROC STDIZE for Fixed-effect Regression

[braam]

I would like to estimate regression with three sets of fixed effects and clustered standard errors. PROC SURVEYREG works, but it has memory issues when there are many fixed effects and/or clusters. So, I decided to use RPOC STDIZE to de-mean my variables. But, I don't think my code is proper. Could anybody help me to point out what is wrong in my code?

My code includes two PROC SURVEYREG.

1) The original data with explicit fixed effects.

2) The de-meaned data (i.e., implicit fixed effects).

I expected the results to be the same, but they are not.

			
		proc freq data= test order=freq; table f1; run;
		proc freq data= test order=freq; table f2; run;
		proc freq data= test order=freq; table f3; run;



* Centering data by f1, f2, and f3;
		data test_centered;
			set test;
			run;

		proc sort data= test_centered; by f1; run;
		proc stdize data= test_centered 
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f1; 
			var dv iv; 
			run;


		proc sort data= test_centered; by f2; run;
		proc stdize data= test_centered
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f2; 
			var dv iv; 
			run;

		proc sort data= test_centered; by f3; run;
		proc stdize data= test_centered
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f3; 
			var dv iv; 
			run;

		proc means data= test; var dv iv; run;
		proc means data= test_centered; var dv iv; run;


		proc surveyreg data= test;
			class f1 f2 f3;
			model dv= iv  f1 f2 f3/ solution;
			run;

		proc surveyreg data= test_centered;
			model dv= iv / solution;
			run;


		proc print data= test; run;

My Original DataSet: 

Obs	f1	f2	f3	dv	iv
1	20202	37	2016	14.1690	4
2	20202	37	2017	14.3602	6
3	20202	37	2018	14.4787	5
4	293110377	38	2016	12.6248	3
5	293110377	38	2017	13.0541	3
6	293110377	38	2018	12.9945	3
7	2020245	28	2016	11.2252	3
8	2020245	28	2017	11.3145	4
9	2020245	28	2018	11.2848	4
10	40023	35	2016	15.6811	2
11	40023	35	2017	15.7506	2
12	40023	35	2018	15.8072	2
13	265160055	36	2016	13.5722	6
14	265160055	36	2017	13.5261	7
15	265160055	36	2018	13.4228	6
16	151340376	28	2016	13.0350	3
17	151340376	28	2017	12.9871	3
18	151340376	28	2018	13.2472	4
19	293110377	38	2016	13.5696	3
20	293110377	38	2017	13.6979	3
21	272200375	38	2016	11.6168	1
22	272200375	38	2017	11.6243	2
23	272200375	38	2018	11.6396	2
24	130376	36	2016	12.4459	1
25	130376	36	2017	12.8828	1
26	130376	36	2018	12.8970	1
27	20342	28	2016	12.9657	4
28	20342	28	2017	13.4190	3
29	20342	28	2018	13.1806	4
30	10421	38	2016	15.4309	2
31	10421	38	2017	15.2439	2
32	10421	38	2018	15.1993	2
33	265160089	33	2016	11.8636	2
34	265160089	33	2017	12.0782	2
35	265160089	33	2018	12.0895	2
36	30111	38	2016	15.1774	5
37	30111	38	2017	15.2131	7
38	30111	38	2018	15.2249	6
39	60435	42	2016	12.8841	2
40	60435	42	2017	12.8980	1
41	60435	42	2018	13.0379	2
42	20023	73	2016	15.8567	5
43	20023	73	2017	15.8304	5
44	20023	73	2018	15.9903	5
45	30245	38	2016	13.9173	8
46	30245	38	2017	15.0267	9
47	30245	38	2018	15.1380	11
48	82560245	73	2016	12.4837	1
49	82560245	73	2017	12.7665	2
50	82560245	73	2018	12.9239	1
51	30198	56	2016	14.5976	2
52	30198	56	2017	14.6309	2
53	30198	56	2018	14.6419	2
54	30322	73	2016	14.6623	1
55	30322	73	2017	14.6135	2
56	30322	73	2018	14.6001	2
57	18510373	38	2016	11.9250	4
58	18510373	38	2017	11.9576	4
59	18510373	38	2018	11.9184	4
60	20111	38	2016	14.6730	8
61	20111	38	2017	14.6226	9
62	20111	38	2018	14.7825	10
63	158380359	73	2017	11.2266	1
64	158380359	73	2018	11.0898	1

[PaigeMiller]

No need to center IV in PROC STDIZE. That's one difference, the models are working on different IV. 

Also, if you center the variables F1 F2 and F3, I think this needs to be done in one big PROC STDIZE such as

proc sort data=test_centered;
    by f1 f2 f3;
run;
proc stdize data= test_centered out= test_centered method= mean 
    oprefix= old sprefix; 
    by f1 f2 f3; 
    var dv; 
run;

Then you ought to be able to fit the model with DV = IV and leave out the F1 F2 F3. (Although this is the equivalent of fitting a 3-way interaction between the variables F1 F2 F3).

Although, one thing I'm not really sure of is that for some reason, I remember that for this to work F2 must be nested in F1, and F3 must be nested in F1*F2, and I can't remember why this is now (however, your variables are not nested).

[PaigeMiller]

Okay, here's my OPINION #2

I think what you have done is the equivalent of the no interaction case between F1 F2 and F3, so maybe your idea is okay. You still don't want to center the variable IV.

I am assigning you a homework project: reduce the size of your data set so there are only a small number of levels of F1 F2 and F3, so it will run through PROC SURVEYREG and get some answers. Then do the PROC STDIZE method on the reduced data set and see if the answers match.

[braam]

@PaigeMiller 

Thanks for your suggestion. I tried centering only the dependent variable, but it didn't help. As you suggested, I reduced my sample to 17 obs. Following this code, the two PROC SURVEYREG gives me:

(1) Coeff on IV= 0.057581 (t= 0.37, p= 0.7137) from the first reg with explicit fixed effects

(2) Coeff on IV= 0.0578481 (t=0.47, p=0.6456) from the second reg with the  centered data

It seems that the coefficients are pretty close, but t-stat and p-value are quite different. In addition, when I use larger sample, the difference gets really substantial.

* Centering data by f1, f2, and f3;
		data test;
			set temp.test;
			where f1 in (20202 293110377 2020245 40023 265160055 151340376) and
					f2 in ( 37 38 28 35 38);
			run;

		proc print data= test;
			run;

		data test_centered;
			set test;
			run;

		proc sort data= test_centered; by f1; run;
		proc stdize data= test_centered 
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f1; 
			var dv iv; 
			run;


		proc sort data= test_centered; by f2; run;
		proc stdize data= test_centered
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f2; 
			var dv iv ; 
			run;

		proc sort data= test_centered; by f3; run;
		proc stdize data= test_centered
			out= test_centered
			method= mean 
			oprefix= old 
			sprefix; 
			by f3; 
			var dv  iv; 
			run;

		proc means data= test; var dv; run;
		proc means data= test_centered; var dv; run;


		proc surveyreg data= test;
			class f1 f2 f3;
			model dv= iv f1 f2 f3/ solution;
			run;
		proc surveyreg data= test_centered;
			model dv= iv / solution;
			run;

Obs	f1	f2	f3	dv	iv
1	20202	37	2016	14.1690	4
2	20202	37	2017	14.3602	6
3	20202	37	2018	14.4787	5
4	293110377	38	2016	12.6248	3
5	293110377	38	2017	13.0541	3
6	293110377	38	2018	12.9945	3
7	2020245	28	2016	11.2252	3
8	2020245	28	2017	11.3145	4
9	2020245	28	2018	11.2848	4
10	40023	35	2016	15.6811	2
11	40023	35	2017	15.7506	2
12	40023	35	2018	15.8072	2
13	151340376	28	2016	13.0350	3
14	151340376	28	2017	12.9871	3
15	151340376	28	2018	13.2472	4
16	293110377	38	2016	13.5696	3
17	293110377	38	2017	13.6979	3

[PaigeMiller]

(1) Coeff on IV= 0.057581 (t= 0.37, p= 0.7137) from the first reg with explicit fixed effects

(2) Coeff on IV= 0.0578481 (t=0.47, p=0.6456) from the second reg with the centered data

Yes, I consider this to be an expected result. The coefficients are esssentially the same, but the degrees of freedom in the model with the centered data ought to be different and so the t-values and p-values ought to be different. Is the sum of squares for error from these two models the same (I would expect it to be since the coefficients are virtually equal)? If so, then I think you have the same model fit, and if you "manually" adjust the degrees of freedom, then you ought to get the same t-value and p-value.