While link functions are not unique for each distribution (see Table 44.13 for the default link functions), the distribution does determine the variance function . This function expresses the variance of an observation as a function of the mean, apart from weights, frequencies, and additional scale parameters. The implied variance functions of the GLIMMIX procedure are shown in Table 44.20 for the supported distributions. For the binomial distribution, n denotes the number of trials in the events/trials syntax. For the negative binomial distribution, k denotes the scale parameter. The multiplicative scale parameter is not included for the other distributions. The last column of the table indicates whether has a value equal to 1.0 for the particular distribution.
Table 44.20: Variance Functions in PROC GLIMMIX
Variance function 


DIST= 
Distribution 


BETA 
beta 

No 
BINARY 
binary 

Yes 
BINOMIAL  BIN  B 
binomial 

Yes 
EXPONENTIAL  EXPO 
exponential 

Yes 
GAMMA  GAM 
gamma 

No 
GAUSSIAN  G  NORMAL  N 
normal 
1 
No 
GEOMETRIC  GEOM 
geometric 

Yes 
INVGAUSS  IGAUSSIAN  IG 
inverse Gaussian 

No 
LOGNORMAL  LOGN 
lognormal 
1 
No 
NEGBINOMIAL  NEGBIN  NB 
negative binomial 

Yes 
POISSON  POI  P 
Poisson 

Yes 
TCENTRAL  TDIST  T 
t 

No 
To change the variance function, you can use SAS programming statements and the predefined automatic variables, as outlined in the following section. Your definition of a variance function will override the DIST= option and its implied variance function. This has the following implication for parameter estimation with the GLIMMIX procedure. When a userdefined link is available, the distribution of the data is determined from the DIST= option, or the respective default for the type of response. In a GLM, for example, this enables maximum likelihood estimation. If a userdefined variance function is provided, the DIST= option is not honored and the distribution of the data is assumed unknown. In a GLM framework, only quasilikelihood estimation is then available to estimate the model parameters.