GMBO fits general models to the binomial odds for binary data.
The basic data in the 
record are 
, 
, and 
, which are, respectively, the number
of trials, the number of cases (which are often called successes in other
contexts), and a vector of covariates. Let 
denote the probability of a case
in a single trial for the record. Then GMBO
computes maximum likelihood estimates in models for the odds ratio of the
form
where 
is a member of the general class
of functions that can be fit by the EPICURE regression programs. The log
likelihood contribution of the cell is most easily
expressed in terms of 
, as in
where 
and 
are, respectively, the
probability or odds for the 
cell evaluated at the
parameter estimates for the current model. The log likelihood is simply the sum
of the 
over all records.
The deviance contribution for the record is
The deviance residual is
and the Pearson residual is
