Hi Stijn,
I went back and took a look at the design matrix attached to your
original message. In order to a have a "DODS" design (to use Doug
Greve's FS terminology) you would need to have separate columns (EVs)
for age and handedness for each of the three groups. As proposed, your
design matrix had only a single column for age and a single column for
handedness, in which case there is only a single "slope" for each
variable applied to all subjects, regardless of their group status.
Reading between the lines of your post, it sounds like you might have
separately demeaned age and handedness by group, and then composed those
values into a single EV for age and a single EV for handedness. If so,
that is a design matrix that makes no sense.
If you want to just model a main effect of age and handedness, then just
demean those variables ACROSS ALL SUBJECTS, if you wish. As I noted in
my other posts, in such a model that doesn't involve group*age or
group*handedness interactions, whether or not you demean gender, age, or
handedness (or any combination of the three) is irrelevant to resulting
inference on contrasts between groups, provided that those contrasts sum
to 0 (which are the types of group contrasts that you were using in your
original post). (Note that if the weights on the group related
contrasts do NOT sum to zero, then whether or not you demean WILL have
an effect on the contrast).
All of this is easy enough to test by creating both types of models and
just running them. I haven't done that with 'randomise' itself, but I
did confirm that all the above statements hold in analogous types of
models run using SAS's PROC GLM. Unless there is something peculiar to
'randomise' that I'm not aware are, I don't see any reason why they
wouldn't hold for 'randomise' as well.
Best,
-MH
On Wed, 2011-02-16 at 10:59 +0000, Stijn Michielse wrote:
> Hi all,
>
> In the original message I already wrote about the confounders having different influence on the three groups. So age, gender and handedness have their own offset and slope in the groups. We didn't match groups. This makes a so called DODS (different offset different slope) design. The design matrix is build up with demeaned confounders by group and padding zero's.
>
> Mark; can you explain a bit more about the two schools of thought?
>
> Cheers,
> Stijn
>
> > Hi Mark,
> > To make this concrete, could you perhaps lay out an example of the type
> > of model that you're thinking of?
> >
> > thanks,
> > -MH
> >
> > On Mon, 2011-02-14 at 19:11 +0000, Mark Jenkinson wrote:
> > Hi Michael,
> >
> > What you say is true if this is the *only* contrast.
> > However, it is common to also have contrasts on
> > the individual group responses, in which case it
> > does make a difference. There are two schools
> > of thought on what the "best" option is, but they
> > are not totally equivalent - only in certain aspects.
> >
> > All the best,
> > Mark
> >
> >
> >
> > On 14 Feb 2011, at 18:29, Michael Harms wrote:
> >
> > > Hi Jesper,
> > > Just to elaborate, in the model that I laid out as an example, you will
> > > indeed get different inference on the intercept regressor if there is a
> > > mean component to other regressors, but in that model, the intercept
> > > regressor was simply modeling the mean, and was not itself a regressor
> > > of interest. In the more typical neuroimaging case involving groups
> > > (say 2 groups, but no explicit column of one's) with gender as a
> > > covariate, then inference on the CONTRAST of the two groups is also
> > > identical regardless of how you model gender. That is, you get
> > > identical inference on the contrast of the group betas, and identical
> > > inference on gender as well, using any gender2 EV of the form: gender2 =
> > > a*gender + b. That is why I originally wrote that there is no need to
> > > demean a term such as gender.
> > >
> > > cheers,
> > > -MH
> > >
> > > On Mon, 2011-02-14 at 14:37 +0000, Jesper Andersson wrote:
> > >> Dear Michael,
> > >>
> > >>> Sorry Mark, but I don't follow you yet. Whether you subtract the mean
> > >>> will certainly affect the beta estimates, but it should have no
> > >>> influence on the resulting inference. That is, say I have a GLM
> > >>> with an
> > >>> intercept column (all one's), and then choose to model a main effect
> > >>> of
> > >>> gender using a column containing 1's for males, and 0 for females.
> > >>> Under that model, the resulting beta is straightforwardly
> > >>> interpreted as
> > >>> the additional amount added for males. Now, that gender column will
> > >>> have a non-zero mean. But as regards the inference on whether the
> > >>> gender term is significant, I will get the exact same p-values
> > >>> regardless of whether I demean the gender column or just use the
> > >>> original.
> > >>
> > >> you are right that you will get the same inference for the gender
> > >> regressor if you demean it or not. BUT you will get different
> > >> inference for the mean regressor (assuming we are modeling the overall
> > >> mean) depending on if you demean the gender regressor or not. In GLM
> > >> any variance that is shared by more than one regressor will not be
> > >> included as part of the inference on either of those regressors. It
> > >> would only get included if you performed an F-test spanning all
> > >> regressors that have a share in that variance.
> > >>
> > >> Hence, it does indeed make a difference if you demean or not. It is
> > >> not always obvious what is the "correct" thing to do. The conservative
> > >> option is typically to not demean.
> > >>
> > >> Does that clarify things?
> > >>
> > >> Jesper
> > >>
> > >>
> > >>> For that matter, I'll get the exact same inference if I
> > >>> multiply the gender column by any constant.
> > >>>
> > >>> cheers,
> > >>> -MH
> > >>>
> > >>> On Mon, 2011-02-14 at 10:22 +0000, Mark Jenkinson wrote:
> > >>>> Dear Michael,
> > >>>>
> > >>>> I'm afraid this is not correct.
> > >>>>
> > >>>> It may be the case for other types of statistical test, but not for
> > >>>> the GLM.
> > >>>> In the GLM (as typically implemented in FSL and other neuroimaging
> > >>>> packages) there is no distinction between continuous and discrete
> > >>>> variables.
> > >>>> Everything is treated as a regressor and you are doing multiple
> > >>>> regression.
> > >>>> The consequence of this is that if two regressors each contain a
> > >>>> non-zero
> > >>>> mean, then any true non-zero mean in the data will tend to be split
> > >>>> across
> > >>>> these regressors (especially as the mean is often a strong
> > >>>> signal). So it
> > >>>> makes a big difference to the estimated parameters (the coefficients
> > >>>> associated with the regressors) whether you remove the mean from one
> > >>>> of them or not. It is true that if you span the same space
> > >>>> (assuming that
> > >>>> some set of regressors adds up to a flat mean). However, it is the
> > >>>> fact
> > >>>> that the mean signal will get shared between the regressors which
> > >>>> causes a problem and *will* have an effect on the parameters
> > >>>> associated
> > >>>> with the "mean" regressors, which is normally what is of interest and
> > >>>> hence a big issue.
> > >>>>
> > >>>> All the best,
> > >>>> Mark
> > >>>>
> > >>>>
> > >>>>
> > >>>> On 11 Feb 2011, at 18:02, Michael Harms wrote:
> > >>>>
> > >>>>> Hi Gwenaelle,
> > >>>>> Why does gender need to be demeaned? You should get identical
> > >>>>> results
> > >>>>> either way because the intercept and gender terms together model the
> > >>>>> same space, regardless of whether gender is demeaned. Demeaning
> > >>>>> really
> > >>>>> only matters when trying to interpret a main effect when that
> > >>>>> effect is
> > >>>>> also included as part of an interaction term with a continuous
> > >>>>> variable.
> > >>>>>
> > >>>>> cheers,
> > >>>>> -MH
> > >>>>>
> > >>>>>
> > >>>>> On Fri, 2011-02-11 at 17:52 +0000, Gwenaëlle DOUAUD wrote:
> > >>>>>> Hi,
> > >>>>>>
> > >>>>>> gender needs to be demeaned. It is not necessary to split the age
> > >>>>>> per group, unless you expect an interaction of age with group...
> > >>>>>>
> > >>>>>> Cheers,
> > >>>>>> Gwenaelle
> > >>>>>>
> > >>>>>>
> > >>>>>>> De: Stijn Michielse
> > >>>>>>> Objet: [FSL] 3 groups randomise
> > >>>>>>> À: [log in to unmask]
> > >>>>>>> Date: Vendredi 11 février 2011, 14h57
> > >>>>>>> Dear FSL Experts,
> > >>>>>>>
> > >>>>>>> The project I'm working on has 258 subjects in the
> > >>>>>>> population divided over 3 groups. Processing in TBSS is
> > >>>>>>> straightforward and I have some questions regarding the
> > >>>>>>> randomise tool.
> > >>>>>>>
> > >>>>>>> Using the randomise tool, I first started creating the
> > >>>>>>> design matrix and contrast matrix (named design.mat and
> > >>>>>>> design.con). For performing a simple T-test everything is
> > >>>>>>> straightforward with contrasts 1 and -1 for corresponding
> > >>>>>>> groups. But things get complicated with the introduction of
> > >>>>>>> confounders. Our groups are not matched since we would like
> > >>>>>>> to include as many individuals as possible. Now we would
> > >>>>>>> like to add age, gender and handedness as a confounder in
> > >>>>>>> the model.
> > >>>>>>>
> > >>>>>>> Checking the JISCMail FSL Archives clue's regarding the
> > >>>>>>> demeaning of confounders pop up. Demeaning per group is
> > >>>>>>> necessary since our groups are not matched. Gender is a
> > >>>>>>> bi-directional (being either female or male) variable and
> > >>>>>>> doesn't need to get demeaned. In our case we have demeaned
> > >>>>>>> handedness since we apply an Oldfield scale (-100 is fully
> > >>>>>>> left-handed, +100 is fully right-handed, with value's in
> > >>>>>>> between). To know sure we do the right thing in analysing, I
> > >>>>>>> attached our design matrix and contrast matrix. In the
> > >>>>>>> design matrix the first column is group 1, second column is
> > >>>>>>> group 2 and the third column is group 3. As you might
> > >>>>>>> notice, row 48 has a group change since this individual is
> > >>>>>>> classified as patient after TBSS processing (some more
> > >>>>>>> changes are seen further on).
> > >>>>>>> For investigating the influence of confounders I added
> > >>>>>>> three extra columns; column 4 for age (demeanded per group),
> > >>>>>>> column 5 for gender (not demeaned) and column 6 for
> > >>>>>>> handedness (demeaned per group). Is it necessary to add
> > >>>>>>> specified columns per group for age, padding the other
> > >>>>>>> groups with 0? Later we may add more confounders if it
> > >>>>>>> survives.
> > >>>>>>>
> > >>>>>>> Executing the randomise tool with the two designs goes like
> > >>>>>>> this:
> > >>>>>>> randomise -i all_FA_skeletonised -o tbss -m
> > >>>>>>> mean_FA_skeleton_mask -d design.mat -t design.con -n 5000
> > >>>>>>> --T2 -V
> > >>>>>>>
> > >>>>>>> Can someone please review the attached design matrix and
> > >>>>>>> contrast matrix and give some advice?
> > >>>>>>>
> > >>>>>>>
> > >>>>>>> Kind regards,
> > >>>>>>>
> > >>>>>>> Stijn Michielse
> > >>>>>>> Research Assistant
> > >>>>>>> Dept. Psychiatry and Neuropsychology
> > >>>>>>> Maastricht University
> > >>>>>>> E-mail: [log in to unmask]
> > >>>>>>
> > >>>>>> --------------------------------------------------------------------
> > >>>>>>
> > >>>>>> Gwenaëlle Douaud, PhD
> > >>>>>>
> > >>>>>> FMRIB Centre, University of Oxford
> > >>>>>> John Radcliffe Hospital, Headington OX3 9DU Oxford UK
> > >>>>>>
> > >>>>>> Tel: +44 (0) 1865 222 523 Fax: +44 (0) 1865 222 717
> > >>>>>>
> > >>>>>> www.fmrib.ox.ac.uk/~douaud
> > >>>>>>
> > >>>>>> --------------------------------------------------------------------
> > >>>>>>
> > >>>>>>
> > >>>>>>
> > >>>>>
> > >>>
> > >
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