[R-sig-ME] parameterization for partly nested design with repeated measurements

Douglas Bates bates at stat.wisc.edu
Fri Nov 12 20:13:23 CET 2010

On Fri, Nov 12, 2010 at 5:09 AM, Kay Cecil Cichini
<Kay.Cichini at uibk.ac.at> wrote:
> dear listers,
> i'd very much appreciate help with setting up the right parameterization for
> the following design:
> 4 regions, in each region 3 to 12 schools, at each school 2-4 classes and
> each class tested before and after intervention, yielding a bimomial outcome
> (pupils that passed / not passed a test).
> i'm interested in differences between before and after (factor = "interv")
> intervention outcomes (X = passed, n = passed + not passed) and in the
> interaction region * interv.
> i tried with:
> glmer (cbind(X, n - X) ~ region * interv + (region | school / class), family
> = binomial)

This model is generating an interaction between the fixed-effects
factor "region" and the random-effects factor "school", which doesn't
make sense because each school occurs within only one region.

The simplest way to establish the desired structure is to create the
region, school and class factors so they follow the "each distinct
structure corresponds to a distinct level of the factor" rule.  For
example, if you call the regions "A", "B", "C" and "D" and you call
the schools "A01", ... "A10", "B01", ..., "B06", "C01", ..., "C12" and
you call the classes "A01a", "A01b", "A01c", ..., "C12d" then you can
specify the model very easily as

glmer(cbind(X, n - X) ~ region * interv + (1|school) + (1|class),
family = binomial)

Most of the confusion about model specification comes from the
unfortunate practice of labeling the schools as "01", ..., "12"
without taking into account that school 1 in region A is not
associated in any way with school 1 in region C.  In other words, all
you need to do is to disambiguate the names of the schools and the

> and with:
> glmer (cbind(X, n - X) ~ region * interv + (1 | school / class), family =
> binomial)
> i'd be happy about comments on the parameterization or any ideas.
> yours,
> kay
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