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03-14-2016 05:55 PM - edited 03-15-2016 09:40 AM

I am using the PROC GENMOD module to do the QML(quasi-maximum likelihood) estimation for some fractional response models. I am aware that GENMOD can provide two different standard errors, empirical and model based. Does any one know what is the difference between those standard errors? And what is the formula and theory behind these two standard errors?

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03-15-2016 10:02 AM

The regular SEs are based on the fitted model, including the working correlation matrix that is used in the GEE approach (i.e., the quasi-likelihood approach). They are consistent if the model and working correlation matrix is correctly specified. The empirical SEs are consistent even if the working correlation matrix is misspecified. Sometimes the empirical SEs are called robust SEs. The formulas are given in the Parameter Estimate Covariances sub-section of the Generalized Estimating Equations section.

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03-15-2016 04:36 PM

Maybe the question is to be understood what the difference is between the standard errors based on the observed information matrix compared to standard errors based on Fishers expected information matrix. The observed information (default) use the the second derivative of the likelihood evaluated at the observed datapoints. Fishers expected is the expected value of the observed information

matrix according to the model. You obtain SE based on Fishers information matrix by adding "EXPECTED" as option in the model line.

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03-15-2016 04:48 PM

This makes a difference too, but this is a different issue from the original question. The so-called empirical estimate of the var-cov matrix of beta-hat is also known as the sandwhich estimate, and it removes (or tries to remove) the effect of certain aspects of the model choice on the estimate. It is sometimes called a robust estimate.

One gets the empical SEs by default with GENMOD (in GLIMMIX, it is not the default). To get the model-based SEs (actually, the SEs based on the model working correlation matrix), one puts MODELSE on the REPEATED statement.

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03-15-2016 04:57 PM

But for my case, since I am using the quasi-likelihood approach, there is no specific distributional assumption for the model, then I think the robust standard error should be the one I need to use? And I think the model-based standard error in GENMOD is the same to the default standard error in NLMIXED, right?