Even though the formulas presented in the GLIMMIX chapter of the SAS/STAT User's Guide, Version 9 are correct, the variance for the Beta and Negative Binomial distribution is incorrectly computed in the GLIMMIX procedure.

In general the GLIMMIX procedure computes Var(Y) using the formula,

   Var(Y)=scale*vf, 

where vf is the variance function.

For example, the variance of the Gamma distribution is

   Var(Y)=Φu²,Φ > 0. 

Here the scale parameter = Φ, and the vf=u².

The GLIMMIX procedure does not handle the Beta and Negative Binomial distributions differently and computes the Var(Y) = scale*vf as usual and is incorrect. Since Var(Y) is the denominator in the PEARSON residual, the PEARSON residual is also incorrectly computed.

For the Beta and Negative Binomial distribution there is an extra parameter in the variance function that is treated as a “scale” parameter by GLIMMIX. The variance function of the Beta distribution is defined as follows:

   Var(Y) = μ(1-μ)/(1 + Φ), Φ > 0

where Φ is treated as a scale parameter by the GLIMMIX procedure for the Beta distribution.

The variance function of the Negative Binomial distribution is defined as follows:

   Var(Y) = μ + ku², k > 0

where k is treated as scale parameter by the GLIMMIX procedure for the Negative Binomial distribution.

Note that Φ and k are not “scale” parameters in the context of the Var(Y)computation because they cannot be factored out in the formula of Var(Y). In other words, Var(Y)=vf is the correct way to compute the variance for the Beta and Negative Binomial distribution.

Operating System and Release Information

Product Family	Product	System	Product Release		SAS Release
			Reported	Fixed*	Reported	Fixed*
SAS System	SAS/STAT	Windows 7 Ultimate 32 bit	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Professional x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Professional 32 bit	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Home Premium x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Home Premium 32 bit	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Enterprise x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Enterprise 32 bit	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows XP Professional	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2008 for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2008	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 Standard Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 Enterprise Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 Datacenter Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft® Windows® for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows XP 64-bit Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 Enterprise 64-bit Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft Windows Server 2003 Datacenter 64-bit Edition	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Microsoft® Windows® for 64-Bit Itanium-based Systems	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		z/OS	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows 7 Ultimate x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows Vista	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Windows Vista for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		64-bit Enabled AIX	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		64-bit Enabled HP-UX	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		64-bit Enabled Solaris	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		HP-UX IPF	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Linux	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Linux for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		OpenVMS on HP Integrity	9.22	9.22	9.2 TS2M3	9.3 TS1M0
		Solaris for x64	9.22	9.22	9.2 TS2M3	9.3 TS1M0

* For software releases that are not yet generally available, the Fixed Release is the software release in which the problem is planned to be fixed.

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Type:	Problem Note
Priority:	high

Date Modified:	2012-01-17 11:51:57
Date Created:	2010-12-31 13:36:43