A brief initial response. My comments are embedded in the original post.
On 22 Jul 2002, [ISO-8859-1] Jo�l Rivest wrote:
> I have repeated measures of weight on some 350 animals. I want to
> investigate the effet of two factors, sex and breed, on the growth
> curve. For this I am using "proc mixed" of sas, with a given
> covariance structure that consider the correlations between the
> measurements (specified in a "repeated" statement). Random effects as
> pen, litter, sire, are specified in a random statement. I want to
> modelise the effect of age on the weigth by a polynomial.
My first reaction is to ask whether you ought to be modeling
this effect by an exponential growth curve. (Such a relation
would be expected over some range of ages, but possibly your
range of ages goes beyond the period of exponential growth.)
But perhaps you are already doing this?
I once encountered growth data (dry weight of chick embryos, ages 6
to 16 days) for which the 4th-degree (quartic) term in a polynomial
was (barely) significant, and for which an exponential growth model
eas clearly appropriate (the graph of log(weight) vs. age was very close
to a straight line).
> How should I test the effect of the sex and breed and their
> interaction with the coefficients associated with the age effect?
> Should I include all interactions sequentially and test them with type
> I sum of square (sequential)? If so, is there a criteria to select
> which of the effect, sex or breed, I should include first?
>
> exemple :
> model weight= sex breed sex * breed
> age age*sex age*breed
> age*age age*age*sex age*age*breed
> age*age*age age*age*age*sexe age*age*age*breed
Depending on how SAS actually calculates the age*age (etc.) terms, you
may run into problems of apparent near-collinearity among these terms.
(To see how troublesome that actually is, ask for a correlations among
all the effects you've listed above. To see how bad it can be, see the
paper cited below on the Minitab web site.)
I would orthogonalize the higher-order interaction terms before putting
them in the model statement. E.g.,
compute agesq = age*age;
regress agesq on age and save the residual as age2;
compute agecu = age2*age;
regress agecu on age and age2 and save the residual as age3.
Then age, age2, age3 all correlate zero with each other;
so use age2 and age3 instead of "age*age" and "age*age*age" in the model.
For more discussion and some details, see my paper "Modelling and
interpreting interactions in multiple regression", one of the "White
papers" on the Minitab web site (at www.minitab.com).
> I didn't include the interactions of the age effects with the term
> sex*breed. Am I OK to do that simplification?
That depends mostly on how strong the age(&c.)*sex*breed interactions
actually are. It is imaginable -- I don't know if it's likely -- that
one or more of these could be strong enough that their omission might
lead to distorted or misleading results for the lower-order effects.
> If at least one interaction between age and sex (or between age and
> breed) is significant (per example sex*age2), I consider I should test
> the sex effect at different ages (in "proc mixed" per exemple, the
> statement : "lsmeans sex/pdiff at age=100" allows to test the sex
> effect at 100 days of age). But to do this, should I remove all non
> significant interactions from the model?
If I were doing it, I'd first plot weight vs. age separately by sex,
but on the same set of axes (or at any rate on axes with the same scales).
This would enable me to see how the difference due to sex changes with
age. Then I might want to model that difference as a function of age,
using means at each sex-by-age cell and probably using multiple
regression.
But if I hadn't modelled age(&c.)*sex*breed, I might also want to plot
weight vs. age for each sex*breed combination (with appropriate labels for
the various points), to see if there were any obvious problems arising
from omitting those interactions. (E.g., if age(&c.) interacted with sex
for one breed but not for another, or if the interactions were in
different directions for one breed compared to another. Or, possibly more
simply, if age(&c.) interacted with breed for one sex but not the other.)
Good luck! -- DFB.
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
.
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