Hi David,
A bit similar to another question I've just answered here, if you want
to test for an interaction between a covariate and sex, then that
needs to be modelled in the design matrix. So you would replace your
column for S1 with two columns, S1 in males, and S1 in females. Then
the interaction is the F-test with -1 over one of these and 1 over the
other, which specifies the null hypothesis that the S1 relationship is
equal in male and female. Similarly for S2.
If S1 and S2 are correlated though (as multiple symptom measures often
are) then you will probably be better off analysing them in two
separate design matrices (you could try complicated orthogonalisation
procedures, but these often end up wrong in my opinion), each with the
sex EVs and age covariate, so that is still adjusted for, but S1 is
not adjusted for S2 or vice versa.
Also, perhaps I should clarify (as I didn't in my previous email) that
demeaning S1 or age (whether overall or separately by gender) will not
effect the male vs female test, or the test of S1, or the S1*sex
interaction. It would only affect tests of mean effects in males,
females, or the overall mean across both sexes. If you are interested
in these means, then I think demeaning all covariates within-sex is
appropriate, which is equivalent to orthogonalising each covariate
with respect to the space collectively spanned by both the sex EVs.
(And also what Steve suggested in the other thread.)
Best,
Ged
On 6 May 2010 01:17, David Shirinyan <[log in to unmask]> wrote:
> Hello
> We want to analyze a dataset with two groups (males, females). Lets say we have 3 subjects per group. We have two symptom measures (s1, s2) as well as age.
> We want to use age as a covariate to remove its effects but want to test for the effects of s1 and s2. Furthermore, we would like to test the interaction between our group variable and s1 and s2.
>
> We have a few questions about how best to model this.
>
> Which regressors should be demeaned?
> Should we set up any orthogonalizations?
>
> As a starting point, we wanted to present our best guess as to the correct way to set this up.
>
> Group Male? Female? S1 S2 Age(demeaned)
> Input1 1 1 0 49 28 -2
> Input2 1 1 0 68 37 0
> Input3 1 1 0 45 40 1
> Input4 2 0 1 42 46 2
> Input5 2 0 1 75 45 2
> Input6 2 0 1 60 52 -3
>
> Age orthogonalized WRT rest of EV’s
>
> Title EV1 EV2 EV3 EV4 EV5
> C1 Male>Female 1 -1 0 0 0
> C2 Female>Male -1 1 0 0 0
> C3 Effect_of_S1 0 0 1 0 0
> C4 Effect_of_S2 0 0 0 1 0
> C5 group X S1 1 -1 1 0 0
> C6 group X S2 1 -1 0 1 0
> C7 S1 X S2 0 0 1 1 0
>
> Thank you in advance for your help.
>
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