The additive-plus-multiplicative model, Υij =
κ
μ. + (αi + βj + ΣλρτριΥρj / ρ=1, has been used to
describe multiplicative interaction in an unreplicated experiment. Outlier effects often appear as interaction in a two-way analysis of variance with one observation per cell. I use this model in the same setting
to study outliers. In data sets with significant interaction, one may be interested in determining
whether the cause of the interaction is due to a true interaction, outliers or both. I develop a new
technique which can show how outliers can be distinguished from interaction when there are simple
outliers in a two-way table. Several examples illustrating the use of this model to describe outliers
and interaction are presented.
I briefly address the topics of leverage and influence. Leverage measures the impact a change in an
observation has on fitted values, whereas influence evaluates the effect deleting an observation has
on model estimates. I extend the leverage tables for an additive-plus-multiplicative model of rank
1 to a rank k model. Several examples studying the influence in a two-way nonreplicated table are
given.
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