A search with Google on keywords "Overdispersion" or "Extra Binomial
Variation" results in a number of relevant references for your case.

Jos Jansen

"nothanks" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> Jay Tanzman <[EMAIL PROTECTED]> wrote in message
news:<[EMAIL PROTECTED]>...
> > nothanks wrote:
> > >
> > > Hi folks,
> > >
> > >   I am trying to develop a reasonable (not 'perfect')
> > > logistic/binary model and would appreciate
> > > critiques/suggestions/references.
> > > I'll start with an example of data:
> > >
> > > Suppose I have 10 cases, each with a binomial outcome
> > > (with n_1, ..., n_10 trials) and let's say 2 predictors,
> > > gender and age.  For example case one has n_1=7 trials and
> > > 2 successes, case 2 has n_2=1 trial and 0 success, etc.
> > >
> > > Suppose the binary outcomes are legal decisions (say success
> > > is 'guilty') and each of the 10 cases corresponds to 10 judges.
> >
> > To clarify, "sex" and "age" are characteristics of the judges?
> >
> > -Jay
>
> Yes.  And there's no jury - think of it as traffic court.
> Also, the actual data has many more predictors with a mix
> of nominal and continuous variables.  So, it is unlikely
> another judge will have the exact same covariate pattern.
> Which leads me to think, perhaps, that each "judge effect"
> is accounted for implicitly by his/her unique covariate
> pattern.

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