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Syntax interaction polynomial term

2 messages · Luca Corlatti, Thierry Onkelinx

#
Dear list members, I am trying to fit some models to investigate the effects of some predictors (weight, age) on fertility.
As the effect of age on fertility is typically quadratic (lower fertility for the extreme age-classes and higher fertility for intermediate age-classes), I fitted the full additive model as:


fertility ~ weight + poly(age, 2, raw=TRUE)


I would also like to fit a model with an interaction term between weight and age, but I fail to understand the correct syntax. Should the interaction be between weight and the full polynomial term:


fertility ~ weight * poly(age, 2, raw=TRUE)


or should it simply be between weight and the age^2?


fertility ~ weight + age + I(age^2) + weight : I(age^2)


Cheers, 
Luca
#
Dear Luca,

This questions has nothing to do with with mixed models. You should have
send it to r-help.

weight * poly(age, 2, raw=TRUE) is equivalent with weight + age + I(age^2)
+ weight : I(age^2) + weight:age. So you need the add the first order
interaction as well.
However you better use the orthogonal polynomials that the raw polynomials.
Because the raw polynomials might be highly correlated. Have a look at this
examples.

age <- 15:50
cor(cbind(age, age ^ 2, age ^ 3))
cor(poly(age, 3, raw = TRUE))
cor(poly(age, 3))
c_age <- scale(age, center = TRUE, scale = FALSE)
cor(cbind(c_age, c_age ^ 2, c_age ^ 3))
s_age <- scale(age, center = TRUE, scale = TRUE)
cor(cbind(s_age, s_age ^ 2, s_age ^ 3))

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

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what the experiment died of. ~ Sir Ronald Aylmer Fisher
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2017-05-16 9:58 GMT+02:00 Luca Corlatti <luca.corlatti at boku.ac.at>: