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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? 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? 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) 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 On Thu, Feb 17, 2011 at 9:33 AM, Thomas Nichols <[log in to unmask]> wrote: > Hi Stijn, Mike, Mark et al, > I'd like to weigh in and reemphasize something Mike said: If you demean, > always demean the variable as a whole before splitting; never demean within > group. There are perhaps some rare exceptions where you would want to > demean within group, but only do this if you're absolutely sure you > understand the impact of this decision (and how it might let nuisance > variability be captured by a variable of interest). > See this post for more on this > https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0906&L=FSL&P=R50284&1=FSL > -Tom > > On Wed, Feb 16, 2011 at 3:10 PM, Michael Harms <[log in to unmask]> > wrote: >> >> 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 >> > > >>>>>> >> > > >>>>>> >> > > >>>>>> -------------------------------------------------------------------- >> > > >>>>>> >> > > >>>>>> >> > > >>>>>> >> > > >>>>> >> > > >>> >> > > > > > > > -- > ____________________________________________ > Thomas Nichols, PhD > Principal Research Fellow, Head of Neuroimaging Statistics > Department of Statistics & Warwick Manufacturing Group > University of Warwick > Coventry CV4 7AL > United Kingdom > > Email: [log in to unmask] > Phone, Stats: +44 24761 51086, WMG: +44 24761 50752 > Fax: +44 24 7652 4532 > > -- Dr. med. Cornelius J. Werner Department of Neurology RWTH Aachen University Pauwelsstr. 30 52074 Aachen Germany