It all depends on the questions that you want to ask. For starters, the
slope estimates will be independent of centering, so I'd expect that any
contrast involving just those slopes (i.e., C*A, C*B, or AGE terms in
your model) will have statistical results independent of centering. Try
it and see if that is the case.
As for contrasts involving the "main" group effect (A or B terms in your
model) the interpretation of those estimates will be affected by the
differential centering within subgroup. For example, the contrast
[0.5 0.5 0 0 0] would average the group response centered at two
different ages (in effect you are averaging the intercepts but the x-
axis is shifted between the two groups). Whether or not that is
meaningful would depend on the question you want to ask.
Your mileage with a "real" statistician may vary. Hopefully one will
chime and correct if the above is off base.
cheers,
-MH
On Wed, 2010-07-07 at 13:49 +0100, Yannis Paloyelis wrote:
> Dear list,
>
> Apologies for reposting message below: essentially my question boils down to: Would you see any problem with centering continuous variable C *within* subgroup (A or B) when there are group differences in C, whether we model the interaction (Columns: A B A*C B*C) or not (Columns: A B C)?
>
> Many thanks for your help,
> Yannis
>
>
> ============================================================================
> Dear list,
>
> A couple of years ago Tom Nichols posted to the list a most informative document ( https://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=SPM;PPOtEw;20080318094435%2B0000) illustrating many common ANCOVA/Multiple regression models. Analyzing my data I have come across the need for one further design (an extension of Tom’s last model (ANCOVA with interaction)) – but I‘d like to check if my interpretations of coefficients and contrasts are accurate. I was wondering if you could spare a few minutes to read through and help me pick any errors. I have used the format Tom had used as I found it to offer great clarity. One essential difference from Tom’s last model is that I have centered the behavioural variable (C) within subgroup, because there are mean differences in C between genotype groups A and B. Would this be correct/necessary? If there are any other design implementations I would be all ears!
>
> I am interested in the increase in response with increasing C, but wish to check if there is C x Group; if interactions were not significant, I suppose I should use a simpler model, with a single C column which would still contain values centred within subgroup?
>
> Thank you all for your help!
>
> Yannis
>
> MULTIPLE REGRESSION, INCLUDING 2 GROUPS, 1 BEHAVIOURAL RESPONSE VARIABLE AND 1 COVARIATE OF NO INTEREST
>
> GROUPS OF SUBJECTS: GENOTYPE A (N=4) AND GENOTYPE B (N=5), ONE CONTINUOUS BEHAVIOURAL VARIABLE: C, centered within subgroup
> COVARIATE OF NO INTEREST: AGE, centered for total group
>
> Design Matrix Parameterization
>
> A B C*A C*B AGE
> 1 0 -20 0 -4
> 1 0 -5 0 6
> 1 0 0 0 -3
> 1 0 25 0 0
> 0 1 0 -20 -5
> 0 1 0 -5 4
> 0 1 0 0 -4
> 0 1 0 10 2
> 0 1 0 15 4
>
> Coefficient interpretation
> Beta 1: Expected response for Group A for C=Group_A_Average(C) and Age= TotalGroup_Average(Age), while accounting for the Group_A_specific linear effect of C and TotalGroup_specific linear effect of Age
> Beta 2: Expected response for Group B for C=Group_B_Average(C) and Age= TotalGroup_Average(Age), while accounting for the Group_B_specific linear effect of C and TotalGroup_specific linear effect of Age
> Beta 3: Expected change in response with increase of 1 unit of C for Group A, for Age= TotalGroup_Average(Age), while accounting for the TotalGroup_specific linear effect of Age
> Beta 4: Expected change in response with increase of 1 unit of C for Group B, for Age= TotalGroup_Average(Age), while accounting for the TotalGroup_specific linear effect of Age
> Beta 5: : Expected change in response with increase of 1 year of Age for TotalGroup,for C = 0 [??]
>
> Contrast Interpretation
>
> 1 [T] [0 0 1 0 0] Increase in response in Group A with increasing C.
> 2 [T] [0 0 0 -1 0] Decrease in response in Group B with increasing C.
> 3 [T] [0 0 1 -1 0] Groups differ in C effects; Group A slope > Group B slope
> 4 [F] [0 0 -1 1 0] Groups differ in C effects; Group A slope > Group B slope OR Group B slope > Group A slope
> 5 [T] [0 0 1 1 0] Average increase in response in Groups A and B with increasing C.
> 6 [F] [0 0 -1 -1 0] Average decrease in response in Groups A and B with increasing C.
> 7 [T] [1 0 0 0 0] Average Group A response at C=Group_A_Average(C) and Age=TotalGroupAverage(Age), while accounting for Group_A_specific linear effect of C and Group_A-specific linear effect of C
>
>
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