Hierarchy Principle:
Significant
product term
!All lower order
components remainII. Interaction
Assessment Stage
Start with HWF model
Use hierarchical backward elimi-
nation:
EViVjbeforeEViInteraction stage flow:
Initial model: E, Vi, EVi, EViVj
Eliminate nonsignificant EViVj termsUse hierarchy principle to specify
for all further models EVi components
of significant EViVj termsOther EVi terms:
Eliminate nonsignificant EVi
terms from models, retaining previous:significant EViVj terms
EVi components
Vi (or ViVj) termsStatistical testing
Chunk testfor entire collection of
interaction terms
If, however, when assessing interaction, a
product term is found significant, theHierar-
chy Principlemust be applied for lower order
components. This principle requires all lower
order components of significant product terms
to remain inallfurther models considered.According to our strategy, we consider interac-
tion after we have specified our initial model,
which must be hierarchically well formulated
(HWF). To address interaction, we use a hier-
archical backward elimination procedure,
treating higher order terms of the formEViVj
prior to considering lower order terms of the
formEVi.A flow diagram for the interaction stage is pre-
sented here. If our initial model contains terms
up to the orderEViVj, elimination of these latter
terms is considered first. This can be achieved
by statistical testing in a number of ways, which
we discuss shortly.When we have completed our assessment of
EViVjterms, the next step is to use the hierar-
chy principle to specify anyEViterms that are
components of significantEViVjterms. Such
EViterms are to be retained in all further mod-
els considered.The next step is to evaluate the significance of
EViterms other than those identified by the hier-
archy principle. ThoseEViterms that arenonsig-
nificantare eliminated from the model. For this
assessment, previously significantEViVjterms,
their EVi components, and all Vi terms are
retained in any model considered. Note that
some of theViterms will be of the formViVjif
the initial model containsEViVjterms.In carrying out statistical testing of interaction
terms, we recommend that a single “chunk” test
for the entire collection (or “chunk”) of interac-
tion terms of a given order be considered first.Presentation: II. Interaction Assessment Stage 207