I had presented the following ANOVA to depict the potential relevance of
interactions, where we are seeking to determine if main effects alone could
be used to represent the essentials of the model with respect to predictions
of values for yland (annual time series):
Df Deviance Resid. Df Resid. Dev F
Value Pr(F)
NULL NA NA 4519 5135.242 NA
NA
cfv 34 517.41791 4485 4617.824
18.68637 0.000000e+000
yland 15 348.6338 4470 4269.191
28.539124 0.000000e+000
mland 9 164.50611 4461 4104.684
22.444086 0.000000e+000
AREA 5 105.90937 4456 3998.775
26.009187 0.000000e+000
yland:mland 117 279.9389 4339 3718.836
2.937919 0.000000e+000
yland:AREA 67 182.53822 4272 3536.298
3.345349 0.000000e+000
mland:AREA 41 90.57283 4231 3445.725
2.712542 2.896125e-008
I thought that the magnitude of the deviance associated with year:month and
year:area, coupled with significance of the F test, indicated a need to
interpret the interactions (i.e. they were potentially relevant in a
pragmatic sense). This assertion was countered with the argument that the
smaller F's associated with the interaction terms indicated that main
effects would be adequate to do the job. Examination of the interactions was
felt to support this argument, as predictions from the interaction model
were mostly variations in degree, not contradictory. However I'm concerned
that the compatability between main effects and interaction model
predictions may be circumstantial (just happened to be true for this
particular example), and that the interpretation of F magnitudes to reflect
relevance of a term might be inappropriate. Opinions?
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