Hi - you'd need to check with Tom to be sure, but I suspect that this
would be valid - though you will then lose the power of FLAME to take
into account the lower-level variances in the highest-level analysis.
Cheers, Steve.
On 27 Jul 2007, at 18:34, James N. Porter wrote:
> Dr. Woolrich-
>
> Thanks for all your assistance on this issue. I have another follow-
> up question.
>
> It is my understanding that bootstrapping/permuting the data and
> using non-parametric analyses will also correct for the
> heteroskedasticity implied by a nested twin pairs design. If this
> is correct, would using randomise to permute and threshold the data
> provide me with robust results in this case? For instance, once I
> obtain single-subject means on the contrast of interest, I use
> avwmerge to concatenate them into a 48 volume 4D image. Then I run:
> randomise -i AllSubjs.nii.gz -o AllSubjs_clust -1 -n 10000 -c 2.3
>
> Would such a procedure suitably control for both heteroskedasticity
> and family-wise error inflation, or am I barking up the wrong tree?
>
> Thanks,
> Jim Porter TRiCAM Lab Coordinator Elliott Hall N437 612.624.3892
> www.psych.umn.edu/research/tricam
>
> Mark Woolrich wrote:
>> Hi Jim,
>>
>>
>>> 1) Would I be correct in believing that choosing FLAME 1 over
>>> Simple OLS in FEAT is analogous to choosing GLS over OLS in a
>>> simple linear regression, and as such, FLAME 1 represents a
>>> method that is going to generate robust results in the face of
>>> violations of regression assumptions such as I have presented here?
>>
>> FLAME (1 or 2) models all of the variance components at each level
>> of the hierarchy (e.g. within-subject variance, between-subject
>> variance). This means that, for example, when inferring at the
>> second level, the within-subject variance from the first level
>> gets used. This is useful because it means that bad subjects with
>> high first-level within-subject variance are downweighted compared
>> to good subjects with low first-level within-subject variance.
>> Hence, FLAME deals with the heteroskedasticity due to differences
>> in the first level within-subject variances in a manner which is
>> analogous to variance weighting in GLS. Note though, that using
>> first level within-subject variances does not mop up your issue
>> with having data from identical twins.
>>
>>> 2) Or, is the Metropolis Hastings procedure not enough, and I
>>> have to use FLAME 1+2 to implement the full Monte Carlo
>>> simulation, which should most definitely be a fully robust
>>> procedure?
>>
>> Just to clarify - FLAME 1 is a fast approximation to the solution
>> based on maximising marginal posterior distributions in a Bayesian
>> framework, whereas FLAME 2 is a slower, more accurate approach
>> which uses the Markov Chain Monte Carlo technique of Metropolis-
>> Hastings. Both deal with heteroskedasticity from lower levels in
>> the model.
>>
>>> 3) Or, are neither of these methods sufficient to overcome
>>> heteroskedasticity, and I need to account for subject clustering
>>> in my design matrices, either by indicating group membership or
>>> by entering extra covariate EVs? (If so, tips on how to best do
>>> this would be much appreciated.)
>>
>> So, as mentioned above, we need to do something more to deal with
>> the fact that you have data from identical twins in the higher
>> level GLM. Otherwise the expected correlation between twins in the
>> data will go unaccounted for and violate the noise assumptions.
>> Whilst I thought we were talking about two sessions for each
>> subject in my last email, the easiest way to deal with the
>> correlations between twins is the same. As I understand it, you
>> want to have EVs to model out the "twin means" by having an EV for
>> each set of twins, where each EV picks out the 2 subjects which
>> make up that twin. These EVs effectively account for the
>> correlation between twins. Then you have a further EV which models
>> your behavioural data.
>>
>> Hope that helps.
>>
>> Cheers, Mark.
>>
>>
>> ----
>> Dr Mark Woolrich
>> EPSRC Advanced Research Fellow University Research Lecturer
>>
>> Oxford University Centre for Functional MRI of the Brain (FMRIB),
>> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
>>
>> Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
>>
>>
>>
>>
>> On 11 Jul 2007, at 15:43, James N. Porter wrote:
>>
>>> Mark-
>>>
>>> Sorry for the confusion; I should have been more explicit (the
>>> old speed for accuracy trade-off). It's not that we have a
>>> repeated-measures design, rather by "twin design" I actually mean
>>> that our sample is composed entirely of sets of monozygotic
>>> (identical) twins, so we fully expect their shared genetic makeup
>>> to be a factor in how much error covariance we need to account
>>> for in our analysis design.
>>>
>>> Since we expect there to be heteroskedasticity within twin pairs,
>>> (I believe) we need to use a clustered/nested design to account
>>> for it. The analogy often used is looking the effect of some
>>> factor (like teaching methods) upon standardized test results
>>> across multiple schools. Even though we may have 150 individual
>>> students in the study, we can't say they are fully independent
>>> and we would need to nest our subjects to account for error
>>> covariance driven by the fact that 50 students come from school
>>> A, 50 from school B, and 50 from school C. Similarly, in our
>>> neuroimaging analysis here we need to account for the error
>>> covariance driven by the fact that our 48 individuals are
>>> clustered in 24 pairs.
>>>
>>> I know that if I were doing a simple linear regression and had
>>> reason to believe there was autocorrelation or clustering in my
>>> data, then I could not get away with using simple Ordinary Least
>>> Squares methods and would have to use Generalized Least Squares
>>> or Weighted Least Squares to impose corrections for inflated
>>> standard errors. When I look at the pull-down menu on the Stats
>>> tab in FEAT, I see Fixed Effects, Simple OLS, FLAME 1, and FLAME 1
>>> +2. It seems to me that they are ordered from least to most
>>> robust to violations of the assumptions of linear regression
>>> (independence of observations, homoskedasticity, no
>>> multicollinearity, etc). So, I guess this brings me back to my
>>> original inquiry:
>>>
>>> 1) Would I be correct in believing that choosing FLAME 1 over
>>> Simple OLS in FEAT is analogous to choosing GLS over OLS in a
>>> simple linear regression, and as such, FLAME 1 represents a
>>> method that is going to generate robust results in the face of
>>> violations of regression assumptions such as I have presented here?
>>>
>>> 2) Or, is the Metropolis Hastings procedure not enough, and I
>>> have to use FLAME 1+2 to implement the full Monte Carlo
>>> simulation, which should most definitely be a fully robust
>>> procedure?
>>>
>>> 3) Or, are neither of these methods sufficient to overcome
>>> heteroskedasticity, and I need to account for subject clustering
>>> in my design matrices, either by indicating group membership or
>>> by entering extra covariate EVs? (If so, tips on how to best do
>>> this would be much appreciated.)
>>>
>>> Thanks again for your assistance,
>>>
>>> Jim Porter TRiCAM Lab Coordinator Elliott Hall N437 612.624.3892
>>> www.psych.umn.edu/research/tricam
>>>
>>> Mark Woolrich wrote:
>>>> Hi James,
>>>>
>>>> Apologies, I am not familiar with some of the language you are
>>>> using. When you say a twin design, are you talking about having
>>>> two FMRI sessions for each subject? In which case you need to do
>>>> something akin to a paired t-test:
>>>> http://www.fmrib.ox.ac.uk/fsl/feat5/
>>>> detail.html#PairedTwoGroupDifference
>>>> where you have EVs to model each of the subject means across the
>>>> two sessions. Then you have alongside those an EV to model your
>>>> behavioural data.
>>>>
>>>> FLAME1 has most of the key benefits associated with FLAME2 with
>>>> respect to using variances from the first level, it just trades
>>>> off a bit of accuracy in the interest of speed - but is
>>>> perfectly adequate for most purposes.
>>>>
>>>> Apologies if I have misunderstood.
>>>>
>>>> Cheers, Mark.
>>>>
>>>> ----
>>>> Dr Mark Woolrich
>>>> EPSRC Advanced Research Fellow University Research Lecturer
>>>>
>>>> Oxford University Centre for Functional MRI of the Brain (FMRIB),
>>>> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
>>>>
>>>> Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
>>>>
>>>>
>>>>
>>>>
>>>> On 10 Jul 2007, at 19:48, James N. Porter wrote:
>>>>
>>>>>
>>>>> I would like to know how to properly account for within-pair
>>>>> variance correlation in FEAT in a twin design. We have measured
>>>>> a continuous variable for all subjects that we are using as a
>>>>> regressor in our fMRI analysis, but we recognize that this
>>>>> variable may not have error that is independent of the twin-
>>>>> pair sampling. In our behavioral analysis in STATA, we can
>>>>> easily implement a design that cluster/nests the twin pairs to
>>>>> obtain robust standard errors. For the neuroimaging analysis,
>>>>> the path is not so clear. I have the following questions:
>>>>>
>>>>> 1) We believe that FLAME 2's full MCMC resampling would
>>>>> automatically produce robust standard errors in this case, but
>>>>> we would like to save time by just running FLAME 1. Does the
>>>>> Metropolis Hastings sampling procedure also result in robust
>>>>> standard errors in this case?
>>>>>
>>>>> 2) At the higher-level, would indicating separate Group
>>>>> membership in FEAT's GLM setup (i.e. Inputs 1&2=Group 1, Inputs
>>>>> 2&3=Group 2, etc) be the same as clustering twin pairs?
>>>>>
>>>>
>>
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---
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
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