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FSL  February 2014

FSL February 2014

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Subject:

Re: First Level GLMat least one EV is (close to) a linear combination of the others.

From:

Mark Jenkinson <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Mon, 17 Feb 2014 06:18:45 +0000

Content-Type:

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Hi Eric,

I think the example you included, with age and sex, is quite confusing as a first-level example since it is so common that these variables are confounds at the second level.  I now see a bit more clearly what you are doing here.

You are correct that the problem stems from the demeaning in the first level.  However, the factor effects approach works well here.  All you need to do is to leave out the grand mean EV, as it plays no role with demeaned data.  So just set up the remaining EVs (with the +1 and -1 values) and you'll be fine.

Note that if you have baseline (rest) conditions as well as the ones you are describing then you can have something more similar to a cell means approach.  In fact, if you have any non-negligible amount of baseline then you should include a "grand mean" EV in the factor effects approach too (but it will only be 1 during the presentation of non-baseline conditions, and 0 when there is baseline).  Most of the teaching about GLM at the first-level, and the examples, assumes that you have a baseline condition.  If that is not true then things are fine, but they seem a bit more tricky because they are a bit different.

I hope this helps.
All the best,
	Mark


On 17 Feb 2014, at 04:37, Eric Walden <[log in to unmask]>
 wrote:

> Thank you Jeanette,
> 
> I am only looking at the first level of analysis with a single subject, all of the GML stuff talks about between subjects analysis and group statistics, as the page notes: "This GLM page attempts to be a cookery book for all common multi-subject designs".
> 
> Things seem to be quite different at the second level.  For example, you can set up an EV that is all ones and measure the group mean.  However, you cannot do something like that at the first level.  Unless I am badly mistaken, if you tried to do that you would be measuring the mean of a mean centered variable, so you would get zero by mathematical definition.  Actually, it might be worse, because you would have a model of the form Y = b1*0, were that last part is a zero which is the mean centered value of an EV that is all ones.  That means that b1 can take on a infinite set of values.
> 
> Later in the FSL GLM page that you point me too it says, "When using a factor effects setup, it is essential that your design includes a grand mean or intercept, i.e. a column of 1s."  I think the essential problem is that you cannot do such a thing at the first level of analysis because FSL does the mean centering automatically.
> 
> When I look at the "Factor effects approach" in the section that you sent me, it looks like what I need to do with my three column format is use the final column to set up 1's and -1's?
> 
> For exampleI might have a three column format file that looks like this:
> 
> Male
> 
> 10 10 1
> 30 10 1
> 
> Which means two male pictures, one starting at 10 seconds and lasting for ten second and one starting at 30 seconds and lasting for 10 seconds.
> 
> Female
> 20 10 1
> 40 10 1
> 
> Instead, I need to set up a single file that looks like this:
> 
> Sex
> 10 10  1
> 20 10 -1
> 30 10 1
> 40 10 -1
> 
> 
> Then I need to do the same for Age.  Then I need to set up an interaction file that has the same times, but the last two columns are multiplied together.
> 
> However, I still have the problem of the mean which is a column of 1's, but is mean centered by FSL and hence becomes a column of zeros.  Or can I set up a three column file that looks like this:
> 
> Mean 
> 10 40 1
> 
> with no convolution.
> 
> The other alternative that you showed me is: "Cell means".  This means that I would break the pictures up into YoungFemale, YoungMale, OldFemale, OldMale.  
> 
> This alternative works for two levels two factors, but as the number of factors and levels increase, the number of EV's increases exponentially (if my math is correct, you would need #factors^#levels different EVs).  This also causes problems if the factors are continuous variables rather than levels.
> 
> The main problem I have is that the model Y= b0 + b1*A + b2*B +b3*A*B should yield exactly the same p-values as the cells model, but Jesper was pretty adamant that looking at the coefficient b1 is not valid.  Of course, that could be due to the centering FSL does--because the part of the intercept that would normally be captured by b0 is captured by the other coefficients.  
> 
> So, I guess the answer to my question is to create an EV for each unique combination of levels and factors (#factors^#levels EVs).
> 
> Right?

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