Purpose
Specify an alternative variance function for poisson (AMFIT) and unconditional logistic (GMBO) regression models. Use of alternative variance functions provides a way to deal with over- or under-dispersion in the outcome variable. The NOVARFUN command is used to remove the effect of a previous VARFUN command and return to the default variance function.
Programs
AMFIT and GMBO with unconditional likelihood
Syntax
VARFUN vname
Arguments and Subcommands
Varfun
Name of a variable that contains the value of alternative variance function for each record at each iteration. The value of this variable is defined using iterative (ITRAN) transformations.
Remarks
In generalized linear models the variance of the expected value
is a function of the expected value. For Poission regression the standard
variance function is the expected value of the number of cases, while for
binomial data for a record with n trials and event
probability p,
the standard variance function is
The simplest alternative variance functions involve multiplicative rescaling of the variance by a constant factor s called a scale factor. To use this type of alternative variance function in EPICURE, it is not necessary to explicitly define an alternative and use the VARFUN command, rather one can use the SCALEFACTOR command to specify the scaling factor.
Variance functions are defined using iterative transformations (specified using the ITRAN command). These transformations are carried out once for each iteration. The user has access to fitted values (%FV) for these computations. One can also make use of specific parameter values stored as named constants using the PARA # as #nc@ commands in the iterative transformation used to define the variance function.
The resulting models are quasi-likelihood models. Convergence should be assessed in terms of the global score function. For these models, the PROFILE and BOUND commands determine bounds based on the quasi-score function. The EPICURE programs do not evaluate the actual quasi-likelihood.
The NOVARFUN command is used to remove a user-defined variance function.
The use of the VARFUN command to fit a quasi-likelihood model to binomial data is illustrated in the BLOTCH.GBO example.