This is my interpretation of the following two models, as clearly as I
can manage, I hope it answers your original questions...
(1) Without covariate interaction: you have an ANCOVA model, the group
difference is adjusted for differences in the covariate. An equivalent
interpretation is that two *parallel* lines are fitted to the two
groups, and the difference in their intercepts (also the difference at
any level of the covariate, since the lines are parallel) is tested.
The contrast will be something like [-1 1 0 0], assuming that the
first two columns model the groups (intercepts), the third is the
covariate, and the fourth is the mean/constant term. Covariate
centering has no effect on the group difference.
(2) With covariate-by-group interaction: you are fitting two
*independent* straight lines to the two groups. The effect of interest
is now (probably) the difference in the slopes of these two lines, and
hence the contrast will be something like [0 0 -1 1 0], assuming the
first two are group intercepts, the next two are group slopes, and the
last is the mean/constant. The difference between the groups, tested
with [-1 1 0 0 0], now depends on the covariate centering options,
since the difference between two *non-parallel* lines depends on where
along the covariate axis you look. Grand mean centering will look at
the difference between lines at the overall mean of the covariate (for
both groups) [I think]; no centering will look at differences at the
intercept (covariate=0) which is usually undesirable [I think].
Centering-by-group will look at the difference between group 1 at the
mean of group 1's covariate, and group 2 at the mean of group 2's
covariate [I think]. Centering-by-group in this model is equivalent to
orthogonalising the covariates with respect to group, so the estimated
group difference will be the same as if the covariate wasn't included,
(i.e. the group difference isn't adjusted in the ANCOVA sense), though
the t-values will not be the same, since residual variance will be
reduced as the covariate can explain some of this.
I hope that makes sense. My apologies for all the [I think]s! The
somewhat confusing nature of the group difference in the model with
covariate interaction is probably one of the motivations for looking
just at the difference in slopes for this model, which won't be
affected by the choice of covariate centering options [I'm reasonably
Paul GRAVEL wrote:
> Dear SPM Experts,
> We are currently doing a PET study comparing 17 healthy controls with 17
> patients. We would like to do an spm analysis that takes into account the
> differences between the 2 groups while covarying a high-novelty seeking
> score. I have looked through the spm archives, spm manuals, PubMed
> archives, to find a similar study, and the closest I got is a post by Sean
> Colloby (posted: Tue, 19 Jun 2001 13:21:41 +0100) with the reply of Dr.
> Friston (posted: Tue, 19 Jun 2001 17:25:43 +0100). However, I am still
> confused about how to setup this analysis, and then the contrast(s);
> apologies! I would mainly have 4 questions...
> Under PET models, I chose "Single-subject: conditions & covariates", then
> I selected the 34 images and set 17 conditions to 1 for the controls, and
> 17 to 2 for the patients. Then I chose one set of covariates and input
> the 34 high-novelty seeking scores. This is where the confusion starts:
> Q1 - Covariate Interaction: By default SPM selects "none" for covariate
> interaction, however intuitively I would have assumed an interaction with
> the condition. How do we decide on what type of interaction to choose?
> Q2 - Covariate Centering: By default SPM selects "around overall mean" for
> covariate centering, Again, I would have assumed a centering around
> condition means. How do we decide on what type of centering to choose?
> Q3 - Contrast: Based on the different options selected above, the design
> matrix will be formed of either 4 or 5 columns. Therefore, how does one
> test for main effect, group interaction, etc...?
> Q4 - Or should I be using a different type of analysis?
> Again, I do apologize for these questions, but at this point my
> statistical knowledge is not up to par. It would really be appreciated if
> anyone could help or refer me to a good source in order to understand the
> Best Regards,
> Paul Gravel
> Neurobiological Psychiatry Unit
> McGill University
> 1033 Pine Avenue West Room 203
> Montreal, Quebec, Canada, H3A 1A1
> Phone: (514) 398-7301
> Fax: (514) 398-4866