Dear Yingying,
According to your message, "randomise" program can not handle two error
> terms (between subjects and within subject). In the future, will
> "randomise" be updated to handle these kind of data?
>
Not in the near future. Repeated measures correlation is difficult enough
in the parametric case; it's even trickier for the non-parametric case.
So, look for feat or fsl_glm handling repeated measures before randomise.
> I tried to use "randomise" to model two time points as repeated measures
> and perform general linear model (GLM) voxel-wise statistical analysis as
> follows:
>
This won't work, not specifically because of a randomise problem, but
because of the limitation of fitting repeated measures with OLS. In the
language Donald set out, this is a "within-subject design" (you have
repeated measures) but you have between-subject effects you want to make
inference on (age, sex, age*sex). Randomise can only handle this kind of
design in the special case of a paired t-test.
Fortunately, it's easy to work around this... you just need to average each
subject's pair of scans, and then run a model with just one scan per
subject, where you can test for the age, sex & age*sex effects you desire.
(You can also construct difference images from each subject's pairs and
fit the same effects, telling you about the impact of these effects on
longitudinal change).
-Tom
> Would you mind taking a look at it?
>
> 8 boys and 8 girls, two scans (average interval 1 year):
> y=sex+age+sex*age.
>
> randomise -i all_FA_skeletonised.nii.gz -o FA_tbss_stats -m mea
> n_FA_skeleton_mask -d design.mat -t design.con -e design.grp -n 1000 --T 2
> -V
>
> Files:
> design.mat
> Column 1: sex group(-1,female;1:male), Column 2: demeaned age in years,
> Column 3: Column 1*Column 2
> Column 4-19: measures
>
> /NumWaves 19
> /NumPoints 32
>
> /Matrix
> -1 -1.2879 1.2879 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 -2.0414 2.0414 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 0.1066 -0.1066 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 0.7285 -0.7285 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> -1 0.1258 -0.1258 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
> -1 0.5888 -0.5888 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> -1 -1.4852 1.4852 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> -1 -1.8003 1.8003 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
> -1 -0.4907 0.4907 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 -1.6961 1.6961 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 1.2189 1.2189 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
> -1 1.8189 1.8189 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> -1 1.2080 1.2080 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
> -1 1.4902 1.4902 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> -1 -0.3455 0.3455 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> -1 -0.6496 0.6496 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
> 1 -1.7071 -1.7071 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
> 1 -0.5126 -0.5126 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
> 1 -0.8578 -0.8578 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
> 1 -2.8414 -2.8414 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> 1 1.1313 1.1313 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> 1 0.7641 0.7641 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
> 1 0.1559 0.1559 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
> 1 1.0025 1.0025 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
> 1 -0.6140 -0.6140 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
> 1 0.4107 0.4107 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
> 1 0.2244 0.2244 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
> 1 -1.7482 -1.7482 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> 1 2.2408 2.2408 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> 1 1.5696 1.5696 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
> 1 1.1943 1.1943 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
> 1 2.0984 2.0984 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
>
>
> design.con
> /ContrastName1 "sex"
> /ContrastName2 "age"
> /ContrastName3 "sex*age"
> /NumWaves 19
> /NumContrasts 3
>
> /Matrix
> 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
>
> design.grp
> /NumWaves 1
> /NumPoints 32
>
> /Matrix
> 1
> 2
> 3
> 4
> 5
> 6
> 7
> 8
> 1
> 2
> 3
> 4
> 5
> 6
> 7
> 8
> 9
> 10
> 11
> 12
> 13
> 14
> 15
> 16
> 9
> 10
> 11
> 12
> 13
> 14
> 15
> 16
>
> Thanks a lot,
> -Yingying
>
>
> ===========================================================
> *Yingying Wang*, Graduate Student, Biomedical Engineering, University
> of Cincinnati.
> Pediatric Neuroimaging Research Consortium, Cincinnati Children's Hospital
> Medical Center.
> MLC 5033, 3333 Burnet Avenue, Cincinnati, OH 45229-3039, United States.
> O: 513-636-3495 C: 513-833-7448 Email: [log in to unmask]
> Blog: http://wang2yg.blogspot.com Homepage:
> http://homepages.uc.edu/~wang2yg
> ===========================================================
>
> >>> Thomas Nichols <[log in to unmask]> 11/16/2011 9:48 AM >>>
> Yingying ( & Donald & Jay)
>
> Sorry to confuse things, but as Donald just pointed out to me off-list,
> you have a 2x2 mixed design and so what I say below (regarding a paired
> t-test) is irrelevant. Donald is correct, since you have one *between*
> subject factor (in addition to a within subject factor) randomise cannot
> fit this data with this model.
>
> The only way to analyze this presently is fit three separate models, as
> Donald and others frequently prescribe: Average the pairs, and fit a
> two-sample t-test to get main effect of group; difference the pairs, and
> fit a one-sample t-test to get the main effect of baseline/follow up; and
> fit the difference data with a two-sample t-test to get the interaction.
>
> Sorry for the mix up!
>
> -Tom
>
>
> n Wed, Nov 16, 2011 at 10:37 AM, Thomas Nichols <[log in to unmask]
> > wrote:
>
>> Hi Donald,
>>
>> The paired t-test is the *one* repeated measures design that randomise (&
>> FEAT, etc) can do exactly. It is crucial that the -e option is used to
>> specify that there are Nsubj exchangeability blocks. That is, under the
>> null hypothesis of no difference between measurement 1 and 2, it is
>> entirely valid to permute *within* *subject*. This is true even if there is
>> strong correlation within subject. Disastrous, uninterpretable results will
>> occur, though, if exchangeability blocks are not set with -e or if they are
>> set incorrectly.
>>
>> In fact, if we were just doing one, single-voxel permutation test, we
>> could *even* omit the subject blocking variables from the model, and let
>> all that between subject variance end up in the denominator of the test
>> stat. The test statistic wouldn't follow any parametric distribution, but
>> (intrasubject) permutation would find the same P-values as when the block
>> variables are included (because the between subject variance corrupting the
>> denominator is the same for every permutation). We *don't* do this because
>> we need test statistics to be comparable over voxels ('pivotal' is the
>> official term), so we use the standard parametric model to create a
>> traditional paired t-test test-statistic.
>>
>> Let me know if you were thinking of some other issue with randomise &
>> repeated measures.
>>
>> -Tom
>>
>>
>> On Tue, Nov 15, 2011 at 4:39 PM, MCLAREN, Donald <
>> [log in to unmask]> wrote:
>>
>>> You can't use randomise for this type of analysis. Randomise only works
>>> when you have one factor (group or time). When you have both, you can't get
>>> the correct permutations.
>>>
>>> Best Regards, Donald McLaren
>>> =================
>>> D.G. McLaren, Ph.D.
>>> Postdoctoral Research Fellow, GRECC, Bedford VA
>>> Research Fellow, Department of Neurology, Massachusetts General Hospital
>>> and
>>> Harvard Medical School
>>> Office: (773) 406-2464
>>>
>>> On Tue, Nov 15, 2011 at 11:37 AM, Yingying Wang <
>>> [log in to unmask]> wrote:
>>>
>>>> You need to use "-e" option to define the exchangeability between the
>>>> two time points. -e design.grp
>>>> If the first 50 points are from your first time points, the second 50
>>>> points are from your second data points. Here is the example design.grp for
>>>> randomise. The two scans are from the same subject. Thus, they might be
>>>> correlated. You need to count for that. Otherwise, program will have
>>>> problem with TFCE correction. It happened to me before.
>>>> design.grp:
>>>> should be the
>>>> 1
>>>> 2
>>>> 3
>>>> ..
>>>> 50
>>>> 1
>>>> 2
>>>> 3
>>>> ...
>>>> 50
>>>>
>>>>
>>>> >>> SUBSCRIBE FSL Jay <[log in to unmask]> 11/15/2011 9:10 AM >>>
>>>>
>>>> Hello,
>>>>
>>>> I am trying to run randomise for repeated measures on baseline (50
>>>> scans) and followup data( 50 scans) as a paired analyses. In my design
>>>> matrix , i have first 3 columns to model group, time, interaction followed
>>>> by 50 columns to model the categorical effect. Hence, the size of design
>>>> matrix is (100 X 53). I have attached the design matrix (design.mat).
>>>>
>>>> When i run randomise on my TBSS data using this design matrix, i get
>>>> the following Warning ( i have pasted the terminal text below ). For some
>>>> reason tfce is not able to handle it. Can you please explain why and what
>>>> is the work around for this situation?
>>>>
>>>>
>>>> ============================================================================
>>>>
>>>> FIU-iMac08:stats jay$ randomise -i all_FA_skeletonised -o tbss -m
>>>> mean_FA_skeleton_mask -d design.mat -t design.con -n 5000 --T2 -V
>>>> randomise options: -i all_FA_skeletonised -o tbss -m
>>>> mean_FA_skeleton_mask -d design.mat -t design.con -n 5000 --T2 -V
>>>> Loading Data:
>>>> Data loaded
>>>> 9.32066e+28 permutations required for exhaustive test of t-test 1
>>>> Doing 5000 random permutations
>>>> Starting permutation 1 (Unpermuted data)
>>>> Starting permutation 2
>>>> Warning: tfce has detected a large number of integral steps. This
>>>> operation may require a great deal of time to complete.
>>>>
>>>>
>>>> ============================================================================
>>>>
>>>> Regards
>>>> Jay
>>>>
>>>
>>>
>>
>>
>> --
>> __________________________________________________________
>> Thomas Nichols, PhD
>> Principal Research Fellow, Head of Neuroimaging Statistics
>> Department of Statistics & Warwick Manufacturing Group
>> University of Warwick, Coventry CV4 7AL, United Kingdom
>>
>> Web: http://go.warwick.ac.uk/tenichols
>> Email: [log in to unmask]
>> Phone, Stats: +44 24761 51086 <+44%2024761%2051086>, WMG: +44 24761 50752<+44%2024761%2050752>
>> Fax: +44 24 7652 4532 <+44%2024%207652%204532>
>>
>>
>>
>
>
> --
> __________________________________________________________
> Thomas Nichols, PhD
> Principal Research Fellow, Head of Neuroimaging Statistics
> Department of Statistics & Warwick Manufacturing Group
> University of Warwick, Coventry CV4 7AL, United Kingdom
>
> Web: http://go.warwick.ac.uk/tenichols
> Email: [log in to unmask]
> Phone, Stats: +44 24761 51086, WMG: +44 24761 50752
> Fax: +44 24 7652 4532
>
>
>
--
__________________________________________________________
Thomas Nichols, PhD
Principal Research Fellow, Head of Neuroimaging Statistics
Department of Statistics & Warwick Manufacturing Group
University of Warwick, Coventry CV4 7AL, United Kingdom
Web: http://go.warwick.ac.uk/tenichols
Email: [log in to unmask]
Phone, Stats: +44 24761 51086, WMG: +44 24761 50752
Fax: +44 24 7652 4532
