FAQ
Why maintain model
hierarchy?
Original
question from an Editor of a peer-reviewed industrial
journal:
“The author of the article you
reviewed disagrees with you objecting to his
response-surface model due to it being non-hierarchical.
He says that ‘a p-value less than 0.05 is typically
considered to be statistically significant, in which
case the non-hierarchical model should be selected;
otherwise, we include non-significant values that cause
the overall model p-value to increase beyond 0.05 in the
ANOVA.’ Please explain for me and him why hierarchical
should be maintained in predictive models.”
Answer:
Models that exclude
hierarchically inferior terms, for example including an
interaction (such as BD) without both parent terms (B
and D), are not well formulated: They lack invariance
to coding for vital fit statistics such as R-squared. In
other words, the analysis will no longer be correct.
This is spelled out by J. L. Peixoto in “A Property of
Well-Formulated Polynomial Regression Models,” The
American Statistician, Feb. 1990, V44, No. 1.*
Also see this 2024 SAS Communities blog on “The What and
the Why of Model Hierarchy.”
I am not very confident in
the model for this proposed publication given that it
becomes insignificant when preserving hierarchy.
However, if provided with the data, I can see whether a
useful hierarchical model can be developed somehow,
e.g., by applying a transformation and/or identifying
outlier(s).
A note for Stat-Ease software
users: You will be warned if your model does not
maintain hierarchy. Just click “Yes” to correct it and
then disregard the added terms not being significant.
(Learn more about model
hierarchy by enrolling in the next Mixture Design for
Optimal Formulations and/or Modern DOE for
Process Optimization workshop.)
*As an owner of two homes—one
in Minnesota and the other in Florida—I enjoyed
reading this because it illustrates the issues of
non-hierarchical models via a data set of temperatures
and their variation due to latitude and longitude
throughout the United States.
