topic Re: Fixed effect with clustered standard errors? proc glm? in SAS Procedures

Fixed effect with clustered standard errors? proc glm?

braam — Fri, 18 Oct 2019 14:37:17 GMT

Dear All,

I was wondering how I can run a fixed-effect regression with standard errors being clustered. I have a panel data of individuals being observed multiple times. I would like to run the regression with the individual fixed effects and standard errors being clustered by individuals. Since I have more than several thousands of individuals, CLASS statement with PROC SURVEYREG is really inefficient, and SAS says insufficient memory. So I don't think I can use PROC SURVEYREG.

Can I achieve this using proc glm or proc model? I searched, but didn't find a clear way to do so. Thanks in advance.

Re: Fixed effect with clustered standard errors? proc glm?

PaigeMiller — Fri, 18 Oct 2019 14:40:43 GMT

Maybe PROC GLM with a WEIGHT statement? https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=statug&docsetTarget=statug_glm_syntax25.htm&locale=en

From the documentation: "If the weights for the observations are proportional to the reciprocals of the error variances, then the weighted least squares estimates are best linear unbiased estimators (BLUE)"

Re: Fixed effect with clustered standard errors? proc glm?

braam — Fri, 18 Oct 2019 15:10:05 GMT

Isn't WLS about heteroscedasticity (i.e., variance) while clustering standard errors is about covariance within a unit (having multiple observations)? I think they are two different issues.

Re: Fixed effect with clustered standard errors? proc glm?

PaigeMiller — Fri, 18 Oct 2019 15:38:31 GMT

How are you thinking about including cluster in any model you would fit?

Re: Fixed effect with clustered standard errors? proc glm?

braam — Fri, 18 Oct 2019 18:04:32 GMT

I'm not sure if I understand your suggestion.

What I would like to do is to include IDs as fixed effects and get standard errors clustered by IDs at the same time. I know it's possible with PROC SURVEYREG, but when I have many ID values, it's practically impossible. So I'm looking for another procedure.

Re: Fixed effect with clustered standard errors? proc glm?

PaigeMiller — Fri, 18 Oct 2019 18:11:10 GMT

@braam wrote:
... and get standard errors clustered by IDs at the same time.

Now this implies that the standard errors clustered by IDs are the output of the regression. Is that correct? I thought the standard errors were inputs to a regression.

Re: Fixed effect with clustered standard errors? proc glm?

braam — Fri, 18 Oct 2019 18:29:32 GMT

Sorry for the confusion. Yes, I would like to 1) have clustered standard errors and 2) include individual-fixed effects.

Re: Fixed effect with clustered standard errors? proc glm?

PaigeMiller — Fri, 18 Oct 2019 18:31:37 GMT

Show us the SURVEYREG code you were thinking of using, even if it doesn't work because there's too many individuals.

Re: Fixed effect with clustered standard errors? proc glm?

braam — Fri, 18 Oct 2019 19:13:33 GMT

This is the code that you requested. In this example, having too many values for Origin would make this type of regression really inefficient, which takes more than several hours for my case/data.

The below is GLM code where I cannot cluster standard errors. I also absorb Origin, rather than estimating its fixed effects. I actually expected the same coefficients on Cylinders from these two approaches, but they are not, which is strange to me.

proc surveyreg data= sashelp.cars;
	cluster Origin;
	class Origin Type;
	model EngineSize= Cylinders Origin Type/ solution;
	run;

proc glm data= sashelp.cars;
	absorb Origin;
	class Type;
	model EngineSize= Cylinders Type/ solution;
	run;

SURVEYREG RESULT

Estimated Regression Coefficients
Parameter	Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	-0.2423962	0.24823069	-0.98	0.4318
Cylinders	0.6195316	0.03299998	18.77	0.0028
Origin Asia	-0.2473363	0.02963121	-8.35	0.0141
Origin Europe	-0.4510775	0.00538821	-83.72	0.0001
Origin USA	0.0000000	0.00000000	.	.
Type Hybrid	-0.1485498	0.10737472	-1.38	0.3007
Type SUV	0.2723754	0.09245885	2.95	0.0985
Type Sedan	-0.0206628	0.05296500	-0.39	0.7341
Type Sports	0.1480223	0.17265540	0.86	0.4816
Type Truck	0.5319361	0.11385004	4.67	0.0429
Type Wagon	0.0000000	0.00000000	.	.

GLM RESULT

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|
Cylinders	0.6292556337		0.01473441	42.71	<.0001
Type Hybrid	-.1535480401	B	0.23825545	-0.64	0.5196
Type SUV	0.2436920500	B	0.08982120	2.71	0.0070
Type Sedan	-.0144629620	B	0.07368536	-0.20	0.8445
Type Sports	0.0949267303	B	0.09199753	1.03	0.3028
Type Truck	0.4970593441	B	0.10899489	4.56	<.0001
Type Wagon	0.0000000000	B	.	.	.

Re: Fixed effect with clustered standard errors? proc glm?

PaigeMiller — Fri, 18 Oct 2019 19:24:57 GMT

This seems to be a problem that I will have to think about, as I don't see an obvious path forward right now. Large number of levels of any class variable do cause this problem where you don't have enough memory or it takes a huge long time.

How were you going to handle the issue that SAS always assigns a standard error of zero to one (or more) of the class levels?

Re: Fixed effect with clustered standard errors? proc glm?

Ksharp — Sat, 19 Oct 2019 12:09:00 GMT

If you have panel data ,Try post it at Forecast forum. also try PROC PANEL .

Re: Fixed effect with clustered standard errors? proc glm?

Rick_SAS — Mon, 21 Oct 2019 15:27:19 GMT

To get the same parameter estimates, you need to specify NOINT in the SURVEYREG procedure:

proc sort data=sashelp.cars out=cars;
by Origin;
run;

proc surveyreg data=cars;
	cluster Origin;
	class Origin Type;
	model EngineSize= Cylinders Origin Type/ noint solution;
        ods select parameterestimates;
	run;

proc glm data=cars;
	absorb Origin;
	class Type;
	model EngineSize= Cylinders Type/ solution;
        ods select parameterestimates;
	quit;

Re: Fixed effect with clustered standard errors? proc glm?

braam — Mon, 21 Oct 2019 16:50:14 GMT

Thanks! I confirmed it! One thing that is interesting to me is that the coefficient on Cylinders is 0.619 in both ways, but their t-stat varies a lot. For surveyreg, t-stat is 18.77 while for glm, t-stat is 46.32.

Is it because absorbing fixed-effects (conceptually demeaning) influences variance-covariance matrix?

Re: Fixed effect with clustered standard errors? proc glm?

Rick_SAS — Mon, 21 Oct 2019 17:45:06 GMT

It is because the variance estimation formulas for survey statistics (like in PROC SURVEYREG) are different from the variance estimation formulas in linear modeling. Although the point estimates are the same, the standard errors are not. The survey variance is inflated because you need to account for the sample design.