Hi Angela,
You had asked if you should demean within group if you wanted to test
the difference between groups in SLOPES. See the 3rd model on
Jeanette's new web page, for the c=[0 0 1 -1] contrast: For that
SPECIFIC CONTRAST whether or not you demean is irrelevant, since as she
says "Mean centering a covariate will never change the estimates for
that covariate". So, for that SPECIFIC CONTRAST, you could choose to
not demean, demean across groups, or even demean within groups, and you
will get identical inference. But demeaning within group is a very
particular and non-standard analysis in general (in terms of its impact
on the interpretation of contrasts on the group means -- i.e., the
1's/0's EVs), thus my previous post.
cheers,
-MH
On Fri, 2011-04-01 at 18:47 +0200, Angela Favaro wrote:
> Hi MH,
>
> this is not simple at all!
> So why in the example of Cornelius below 'demeaning within groups' was
> right? Which is the difference with my example?
>
> Thanks!
>
> Angela
>
>
>
>
> > Hi Angela,
> >
> > Just to keep it simple, as general advice, one should not ever demean
> > separately within group UNLESS you know exactly what implications this
> > has on the analysis. In the case of your specific example of testing
> > for differences between groups in the slopes of their continuous
> > covariate, that is NOT a reason for demeaning separately within group.
> >
> > cheers,
> > -MH
> >
> > On Fri, 2011-04-01 at 13:46 +0200, Cornelius Werner wrote:
> >> On Fri, Apr 1, 2011 at 11:28 AM, Angela Favaro <[log in to unmask]>
> >> wrote:
> >> > Hi Cornelius,
> >> > thank you for your reply.
> >> > However, you did not completely answer to my doubts.
> >> > Let me make an example:
> >> >
> >> > I am studying a brain area whose connectivity (resting state) seems to
> >> > show a positive correlation with a cognitive variable in the patient
> >> group
> >> > and a negative correlation with the same variable in the control
> >> group.
> >> > This cognitive variable also differ between groups.
> >> > If I want to test the differences between groups in SLOPES, I will
> >> demean
> >> > within groups. Is it right?
> >>
> >> If the intercept is of no interest and you are sure not to affect your
> >> contrasts of the mean regressors in an invalid way, I'd say yes.
> >>
> >> > If I want to test the differences between groups in connectivity
> >> removing
> >> > the effects of the cognitive variable (suppose this has some sense), I
> >> > will demean across groups or (according to type of variable) I can not
> >> > demean at all. Right?
> >>
> >> Again, I'd say yes.
> >>
> >> > For the second question: in a design with two groups and a covariate
> >> of
> >> > interest demeaned across groups. Do I need to use the -D option? And
> >> what
> >> > if the demeaning is within groups?
> >>
> >> If you have regressors modelling the mean (say, one regressor with 1's
> >> for each patient and 0's for controls, and a second regressor with the
> >> other way around), you should not need the -D option. If there is no
> >> mean regressor but only one regressor demeaned across groups, you
> >> probably need the -D flag, as far as I got it. If you demeaned within
> >> groups in this setting, you probably also need the -D flag, but you
> >> will be testing for slopes only - any difference of the mean will not
> >> appear in your test statistics. If the lines were parallel in that
> >> setting, but miles apart, you wouldn't see it.
> >> Before taking this all for true, I'd advise also checking on all the
> >> previous posts in other threads - might be I missed something myself.
> >>
> >> Hope that helps,
> >> Cornelius
> >>
> >> > Thanks!
> >> > Angela
> >> >
> >> >
> >> >> Hi Angela,
> >> >>
> >> >> let's see if I got it right.
> >> >>
> >> >> 1) Besides testing for slopes, I am also interested in average group
> >> >> differences. Thus, if ages weren't matched, I would be introducing a
> >> >> confound, i.e., any effect introduced by progressing age (e.g. task
> >> >> speed) would also influence the group mean. As long as I demean
> >> ACROSS
> >> >> groups, this will not influence the *group means* and their contrasts
> >> >> - in the GLM, any *shared* variability simply disappears (and will
> >> >> lower "sensitivity" of either contrast, and rightly so. Teaches me to
> >> >> match groups the next time, as Jesper put it two days ago).
> >> >> If, on the other hand, I demeaned only within groups, I would not
> >> >> correct for the fact that there was a significant contribution of the
> >> >> factor "age" to either group. All variability due to the difference
> >> of
> >> >> age means would be soaked up by the group means and their contrasts.
> >> >> Therefore, if these group contrasts showed something significant, it
> >> >> might have been just due to the age difference (group a is slower
> >> than
> >> >> b, but also happens to be the older one!), but not due to treatment
> >> or
> >> >> diagnosis, or whatever I was actually interested in.
> >> >>
> >> >> 2) As far as I got it, if you are only interested in correlations
> >> with
> >> >> a (demeaned) covariate and did not model any group mean, you also
> >> >> should demean the data before "randomise"ing. As an example: running
> >> >> randomise on VBM data of a depressed patient cohort, looking for GM
> >> >> changes correlating with a suicidal ideation score ranging from -5 to
> >> >> +5, mean 0. In this case, randomise -D will do the demeaning of the
> >> >> DATA (not the covariates) for you, saving you the effort of running
> >> >> fslmaths on the data.
> >> >>
> >> >> If anything of this is wrong, I am sure one of the other contributors
> >> >> will point it out rather quickly and I'll have lost posting rights
> >> for
> >> >> 4 weeks or so :-)
> >> >>
> >> >> Cheers,
> >> >> Cornelius
> >> >>
> >> >> On Thu, Mar 31, 2011 at 11:36 PM, Angela Favaro
> >> <[log in to unmask]>
> >> >> wrote:
> >> >>> Dear FSL Masters,
> >> >>> this discussion has been very helpful for me.
> >> >>> But I still have two doubts:
> >> >>> 1. Demeaning within groups is more an exception than a rule, but it
> >> is
> >> >>> the
> >> >>> correct thing when I want to test differences between slopes (and
> >> not
> >> >>> differences between groups). Is it correct?
> >> >>> In the example below the two groups have a similar age. What happens
> >> if
> >> >>> the covariate differs in the two groups?
> >> >>>
> >> >>> 2. What continues to be unclear to me is the use of the -D option in
> >> >>> randomise. When is it necessary/advisable to use it? Only in one
> >> group
> >> >>> covariate analysis?
> >> >>>
> >> >>> Thank you
> >> >>>
> >> >>> Angela
> >> >>>
> >> >>>
> >> >>>
> >> >>>> Yeah, that's what I thought. And basically that's why I asked in
> >> the
> >> >>>> first place :-)
> >> >>>> But thanks for all the contributions to this topic. I believe I
> >> have
> >> >>>> an idea on how to go about it, now.
> >> >>>> Best regards,
> >> >>>> Cornelius
> >> >>>>
> >> >>>> On Thu, Mar 31, 2011 at 5:06 PM, Michael Harms
> >> <[log in to unmask]>
> >> >>>> wrote:
> >> >>>>> Just wanted to chime in that demeaning the performance EV
> >> separately
> >> >>>>> within group is a rather unique case that is specific to this
> >> >>>>> particular
> >> >>>>> post.
> >> >>>>>
> >> >>>>> Recent posts by Jesper (just yesterday), Jeannette, Tom, and
> >> myself
> >> >>>>> have
> >> >>>>> all advised that, in general, one should demean across all
> >> subjects
> >> >>>>> (NOT
> >> >>>>> within group separately).
> >> >>>>>
> >> >>>>> Given the recent posts on this, I thought it was worth making
> >> explicit
> >> >>>>> that demeaning within groups is not a "typical" situation.
> >> >>>>>
> >> >>>>> And as a matter of good reporting practice, any time that
> >> demeaning is
> >> >>>>> performed separately within group, rather than across all
> >> subjects,
> >> >>>>> that
> >> >>>>> should be noted (and justified) very explicitly in any
> >> presentation of
> >> >>>>> the ensuing results.
> >> >>>>>
> >> >>>>> cheers,
> >> >>>>> -MH
> >> >>>>>
> >> >>>>> On Thu, 2011-03-31 at 08:42 +0100, Stephen Smith wrote:
> >> >>>>>> Hi
> >> >>>>>>
> >> >>>>>> On 30 Mar 2011, at 11:30, Cornelius Werner wrote:
> >> >>>>>>
> >> >>>>>> > Hi,
> >> >>>>>> >
> >> >>>>>> > sorry to revive such a well-worn topic. But there is something
> >> I
> >> >>>>>> did
> >> >>>>>> > not quite get so far.
> >> >>>>>> > As an example, I am examining a patient cohort and a control
> >> cohort
> >> >>>>>> > in
> >> >>>>>> > a Dual Regression setup (resting state data). Patients and
> >> controls
> >> >>>>>> > are matched for age and gender. They obviously differ in
> >> diagnosis,
> >> >>>>>> > but also in one performance score. I am interested in basic
> >> group
> >> >>>>>> > differences and the differential correlation of connectivity
> >> >>>>>> > strength
> >> >>>>>> > of several RSNs with performance. For the final randomise-step,
> >> my
> >> >>>>>> > design matrix has a column for group mean "patient" and one for
> >> >>>>>> > "controls" (consisting of 1, padded with zeroes where
> >> applicable),
> >> >>>>>> > and
> >> >>>>>> > two separate columns for age (as a confounder) - one for each
> >> >>>>>> group,
> >> >>>>>> > respectively, because an age*group interaction on
> >> connectivities
> >> >>>>>> > could
> >> >>>>>> > not be excluded a priori. As I was modelling the group mean
> >> >>>>>> > separately, only the slopes associated with age were tested. Is
> >> >>>>>> that
> >> >>>>>> > correct so far?
> >> >>>>>>
> >> >>>>>>
> >> >>>>>> I think so - sounds fine.
> >> >>>>>>
> >> >>>>>> > As the age means did not differ (tested beforehand),
> >> >>>>>> > does it matter if I demeaned within group or across groups?
> >> >>>>>> > Shouldn't
> >> >>>>>> > the intercept be modelled by the group mean regressor, in any
> >> case?
> >> >>>>>> > Following Tom's last post, I'd probably demean across groups.
> >> >>>>>> >
> >> >>>>>> > The next thing is even more unclear to me:
> >> >>>>>> > Due to an expected group*performance interaction (i.e. steeper
> >> >>>>>> slope
> >> >>>>>> > of increases in connectivity along with better performance in
> >> >>>>>> > contrast
> >> >>>>>> > to the other group), also the performance scores are split.
> >> BUT:
> >> >>>>>> > should I demean?
> >> >>>>>>
> >> >>>>>>
> >> >>>>>> Yes - if you want to compare the *slopes* between the two groups,
> >> >>>>>> demean the performance scores within group before padding with
> >> zeros,
> >> >>>>>> for each group's performance EV.
> >> >>>>>>
> >> >>>>>> > And if so, within groups, or across groups? In this
> >> >>>>>> > case, mean differences in performance are believed to be *due
> >> to*
> >> >>>>>> > diagnosis - therefore, variability associated with the mean
> >> should
> >> >>>>>> > go
> >> >>>>>> > to the group regressor, shouldn't it? In this case, I'd be
> >> inclined
> >> >>>>>> > to
> >> >>>>>> > demean in order not to affect the group mean regressor
> >> negatively,
> >> >>>>>> > and
> >> >>>>>> > to demean within groups, because of the (clearly) attributable
> >> mean
> >> >>>>>> > variability...?!
> >> >>>>>> >
> >> >>>>>> > Example:
> >> >>>>>> >
> >> >>>>>> > EV1: Patient mean
> >> >>>>>> > EV2: Control mean
> >> >>>>>> > EV3: Patient age (demeaned across groups - EV of no interest)
> >> >>>>>> >
> >> >>>>>>
> >> >>>>>>
> >> >>>>>> I presume you mean demeaned within group, then padded with zeros.
> >> >>>>>>
> >> >>>>>>
> >> >>>>>> Cheers.
> >> >>>>>>
> >> >>>>>> > EV4: Control age ( " )
> >> >>>>>> > EV5: Patient performance score (demeaned within patients)
> >> >>>>>> > EV6: Control performance score (demeaned within controls)
> >> >>>>>> >
> >> >>>>>> > Patients>controls: 1 -1 0 0 0 0
> >> >>>>>> > Controls>patients: -1 1 0 0 0 0
> >> >>>>>> > Slope(performance score) patients > Slope(performance score)
> >> >>>>>> > controls:
> >> >>>>>> > 0 0 0 0 1 -1
> >> >>>>>> > Slope(performance score) controls > Slope(performance score)
> >> >>>>>> > patients:
> >> >>>>>> > 0 0 0 0 -1 1
> >> >>>>>> >
> >> >>>>>> > Please don't hit me - I'm having a hard time getting my head
> >> around
> >> >>>>>> > this :-)
> >> >>>>>> > Cheers,
> >> >>>>>> > Cornelius
> >> >>>>>> >
> >> >>>>>> >
> >> >>>>>>
> >> >>>>>> ---------------------------------------------------------------------------
> >> >>>>>> Stephen M. Smith, Professor of Biomedical Engineering
> >> >>>>>> Associate Director, Oxford University FMRIB Centre
> >> >>>>>>
> >> >>>>>> FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
> >> >>>>>> +44 (0) 1865 222726 (fax 222717)
> >> >>>>>> [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
> >> >>>>>> ---------------------------------------------------------------------------
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>>
> >> >>>>>
> >> >>>>
> >> >>>>
> >> >>>>
> >> >>>> --
> >> >>>> Dr. med. Cornelius J. Werner
> >> >>>> Department of Neurology
> >> >>>> RWTH Aachen University
> >> >>>> Pauwelsstr. 30
> >> >>>> 52074 Aachen
> >> >>>> Germany
> >> >>>>
> >> >>>>
> >> >>>
> >> >>
> >> >>
> >> >>
> >> >> --
> >> >> Dr. med. Cornelius J. Werner
> >> >> Department of Neurology
> >> >> RWTH Aachen University
> >> >> Pauwelsstr. 30
> >> >> 52074 Aachen
> >> >> Germany
> >> >>
> >> >>
> >> >
> >>
> >>
> >>
> >
> >
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