Re: st: When number of regressors greater than the number of clusters in OLS regression

[Steven Samuels <sjhsamuels@earthlink.net>]

Thanks Mark. I've been thinking that the data were not *sampled* as  
clusters. Since they were not, I erroneously assumed that there would  
not be cluster effects. I agree clustered effects should be  
considered. As Vince Wiggins stated in http://www.stata.com/statalist/ 
archive/2005-10/msg00594.html , "We can use the [robust] covariance  
matrix to test any subset of joint hypotheses that does not exceed  
its rank." Thus Divya can get valid standard errors for single  
coefficients, if she adds states as clusters, and can probably make  
most of the inferences she is interested in.

-xtreg- offers some intriguing possibilities, for it would  
distinguish between state-level and district-level predictors of the  
same kind. Of course statistics from neighboring districts may be  
spatially correlated, opening up a completely different area of  
analysis.

Perhaps the best advice to Divya that I can give, in addition to Mark's:

Clarify your purpose--is the study exploratory ("find a good  
predictive model")? Or are you testing hypotheses about certain  
predictors? If your analysis is exploratory, consider holding out a  
random set of districts or states on which to test the fit of your  
"best" models. If you are interested in certain predictors, than  
others are potential effect modifiers and confounders. You probably  
don't need them all. Do you have 25 predictors because you know they  
are all important from other studies?  The more unnecessary  
predictors you have in one model, the more difficult it will be to  
tease out the truly important ones.

-Steve



On Sep 1, 2008, at 6:00 PM, Schaffer, Mark E wrote:


> Whether or not you need to use cluster-robust depends on whether you
> think your data have a problem that cluster-robust can address, namely
> (1) the error terms in your equation are correlated within states
> because of unobserved heterogeneity (so the iid assumption fails), but
> (2) the error terms are not correlated across states.
>
> A good example would be whether you are looking at something that is
> affected by state-level regulation, i.e., the laws regulating it vary
> from state to state, but you don't have variables that control for  
> this
> somehow.
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