sas >> Heteroscedasticity PROC REG

by filipa.fig » Thu, 10 Jan 2008 01:00:45 GMT

Hi,
I estimated a linear model using the PROC REG and I did the test of heteroscedasticity using the option SPEC. The log returned the following warning: "The average covariance matrix for the SPEC test has been deemed singular which violates an assumption of the test. Use caution when interpreting the results of the test.". The test rejected the null hypothesis. In that case, What I need to do? Can I correct the heteroscedasticity with the option ACOV? Can I read the statistics associated to the parameters?
Best Regards
Filipa


sas >> Heteroscedasticity PROC REG

by stevedrd » Thu, 10 Jan 2008 21:43:02 GMT


Filipa,

It's difficult to offer a solution without knowing something about the model you are trying to fit. Everything I say below assumes that all independent variables are continuous, and that no grouping or design variables are involved (if so, then PROC MIXED or GLIMMIX might be a better tool).

If the average covariance matrix is singular, my first guess would be that some of the regressors are not independent. In any case, the test for homogeneity isn't valid. The test is also pretty sensitive to the assumption of multivariate normality of the residuals. Check out the thread "Q: "proc glm" and testing for the equality of variances" for more discussion on this subject--especially Robin High's response where she quotes Box.

According to the documentation, specifying both SPEC and ACOV should produce two outputs: "When you specify the SPEC option, tests listed in the TEST statement are performed with both the usual covariance matrix and the heteroscedasticity consistent covariance matrix. Tests performed with the consistent covariance matrix are asymptotic. For more information, refer to White (1980)." So estimates of the betas are unchanged, only their standard errors will differ.

Personally, I'd do this, look at the results, and hope that the conclusions were not really different. Linear models are pretty robust to the assumption of equal variance. If the results of the tests are very different, I would explore the nature of the heterogeneity (plotting residuals, etc.). Perhaps a simple transformation will alleviate the problem. If that doesn't clear things up, you can always force homogeneity by standardizing. By then, you have the problem of interpreting the results from the transformed space back to the design space, and regression on standardized variables very often has an interpretation that is quite different from regression on the actual observations.

Looking over this response, it doesn't seem very helpful. More information regarding the model and any distributional assumptions on the variables would help.

Steve Denham
Associate Director, Biostatistics
MPI Research

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----- Original Message ----
From: SUBSCRIBE SAS-L Filipa < XXXX@XXXXX.COM >
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Sent: Wednesday, January 9, 2008 12:00:45 PM
Subject: Heteroscedasticity PROC REG

Hi,
I estimated a linear model using the PROC REG and I did the test of heteroscedasticity using the option SPEC. The log returned the following warning: "The average covariance matrix for the SPEC test has been deemed singular which violates an assumption of the test. Use caution when interpreting the results of the test.". The test rejected the null hypothesis. In that case, What I need to do? Can I correct the heteroscedasticity with the option ACOV? Can I read the statistics associated to the parameters?
Best Regards
Filipa


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