Agresti uses the letters G (sex
), R (race
),
A (alcohol
), C (cigarette
), M (marijuana
) to refer to the table variables,
and this usage is followed in the examples below.
Background variables include sex
and race
of the
respondent (GR), typically treated as explanatory, so that any
model for the full table should include the term sex:race
.
Models for the reduced table, collapsed over sex
and race
are not entirely unreasonable, but don't permit the estimation
of the effects of these variables on the responses.
The full 5-way table contains a number of cells with counts of 0 or 1,
as well as many cells with large counts, and even the ACM table
collapsed over GR has some small cell counts. Consequently,
residuals for these models in mosaic displays are best represented
as standardized (adjusted) residuals.