You can answer all 5 of your questions with the 4-EV (interaction) model:
1) [0 0 1 0] (i.e., is the slope of the Patients behavioral EV positive?)
2) [0 0 0 1] (i.e., is the slope of the Controls behavioral EV positive?)
3) [0 0 1 -1] (i.e., is the Pat-Con slope difference positive?)
4) [1 0 0 0] (i.e., is the intercept for Patients > 0, controlling for
behavior?)
5) [0 1 0 0] (i.e., is the intercept for Controls > 0, controlling for
behavior?)
Make sure you mean center the behavioral covariate across all subjects
prior to splitting the behavioral data into separate EVs for Patients and
Controls.
cheers,
-MH
--
Michael Harms, Ph.D.
-----------------------------------------------------------
Conte Center for the Neuroscience of Mental Disorders
Washington University School of Medicine
Department of Psychiatry, Box 8134
660 South Euclid Ave. Tel: 314-747-6173
St. Louis, MO 63110 Email: [log in to unmask]
On 7/30/13 11:30 AM, "Benjamin Philip" <[log in to unmask]> wrote:
>I do see some effects of [0 0 1 -1], so there is a significant
>interaction effect. Not in the brain areas we care about, but still.
>
>Apologies for the arbitrary symbology; I'm trying to find ways to express
>this without getting bogged down in dense strings of words. * means
>"correlated with". To clarify, the most important questions for my
>analysis are,
>1) "What areas show significant behavior-correlated activity among
>patients?" (P*b)
>2) " .... among controls?" (C*b)
>3) "What areas show more behavior-correlated activity among patients than
>among controls?" (P*b)-(C*b)
>Secondary questions include:
>4) "What areas are active for this task in a behavior-independent
>fashion, among patients?" (P controlling for b)
>5) " ... among controls?" (C controlling for b).
>
>Thus, in the three-column model, [1 0 0] answers #4 but not #1. For
>#1-2, is the best method just to do the analysis independently for each
>group, with one EV (behavior)? Or is there a way to do #1 and #2 in the
>same model?
>
>The Jeanette Mumford page looks very helpful, thanks for pointing me
>towards it. If I understand both you and her, my #3 may indeed be this
>uninterpretable-for-my-data [1 -1 0 0]. I'm not crushed that it's
>uninterpretable, though; I have some nice clean ROI data to back all this
>up.
>
>Thanks,
>-Benjamin Philip
>
>P.S: The "implication that intercept depends on slope" was from the
>analogy of fitting lines - my interpretation assumed a constant mean (in
>which case a change of slope would produce a change in intercept), my
>mistake.
>
>On Tue, 30 Jul 2013 14:56:52 +0000, Harms, Michael <[log in to unmask]>
>wrote:
>
>>If the interaction effect is significant (i.e., differing slopes), then
>>yes, the difference between groups (y-distance between the two lines)
>>itself differs as a function of where you are along the covariate, and in
>>that case interpreting the [1 -1 0 0] contrast is indeed more
>>complicated,
>>and you're probably best to stay away from it.
>>
>>I don't know where I implied that the intercept depends on the slope, but
>>I didn't intend to. The intercept and slope betas are independent
>>parameters.
>>
>>In the 3-column model, [1 0 0] is testing whether the intercept of Grp1
>>differs from zero. In effect, you are testing whether Grp1 is non zero
>>while "controlling" for the behavioral variable. I'm not sure what you
>>mean by (P*b).
>>
>>Jeanette Mumford's web page on mean centering has some illustrations that
>>may further help.
>>
>>cheers,
>>-MH
>>
>>--
>>Michael Harms, Ph.D.
>>
>>-----------------------------------------------------------
>>Conte Center for the Neuroscience of Mental Disorders
>>Washington University School of Medicine
>>Department of Psychiatry, Box 8134
>>660 South Euclid Ave. Tel: 314-747-6173
>>St. Louis, MO 63110 Email: [log in to unmask]
>>
>>
>>
>>
>>On 7/30/13 9:33 AM, "Benjamin Philip" <[log in to unmask]> wrote:
>>
>>>Interesting! Your [1 -1 0 0] suggestion goes against the webpage's
>>>advice
>>>that "Importantly, this model should only be used to interpret the
>>>interaction effect." - but perhaps I misunderstood that sentence, I
>>>thought it meant the model only applied to difference-between-slopes.
>>>
>>>The results of this intercept-test seem to pass my little "empirical
>>>test" (it's consistent with our ROI results too) so this may be what I'm
>>>looking for. But I'm still a bit uncertain on the logic: wouldn't a [1
>>>-1 0 0] model remove the effect of behavior-correlation, via the zeros
>>>in
>>>those last two columns? That seems at odds with your description, which
>>>implies that the intercept depends on the slope (because that is what
>>>intercepts are wont to do). At this point I think you're right, I just
>>>want to make sure I understand it properly.
>>>
>>>As for the separate groups stuff: I had thought my 3-column model would
>>>allow (P controlling for b) via [1 0 0], and (P correlated with b) via
>>>[1
>>>0 1]... but if I was wrong, how would you recommend getting those (P
>>>controlling for b) and (P*b) effects for each group?
>>>
>>>Thanks,
>>>-Benjamin Philip
>>>
>>>
>>>On Tue, 30 Jul 2013 02:17:52 +0000, Harms, Michael <[log in to unmask]>
>>>wrote:
>>>
>>>>Also, I just took a look your Dropbox README, and part of the issue is
>>>>that in your comparison model with just 3 total EVs (grp1 grp2 Behav),
>>>>the
>>>>contrasts [1 0 1] and [0 1 1] are not meaningful contrasts. In such a
>>>>model, the meaningful potential contrasts are [1 0 0], [0 1 0], [1 -1
>>>>0],
>>>>and [0 0 1] (and the negative version of each of those).
>>>>
>>>>cheers,
>>>>-MH
>>>>
>>>>--
>>>>Michael Harms, Ph.D.
>>>>
>>>>-----------------------------------------------------------
>>>>Conte Center for the Neuroscience of Mental Disorders
>>>>Washington University School of Medicine
>>>>Department of Psychiatry, Box 8134
>>>>660 South Euclid Ave. Tel: 314-747-6173
>>>>St. Louis, MO 63110 Email: [log in to unmask]
>>>>
>>>>
>>>>
>>>>
>>>>On 7/29/13 9:09 PM, "Harms, Michael" <[log in to unmask]> wrote:
>>>>
>>>>>
>>>>>The two group interaction model is equivalent to fitting two lines to
>>>>>the
>>>>>data.
>>>>>The first two EVs fit the intercept for the two groups. And the betas
>>>>>for
>>>>>EVs 3 and 4 fit the slope (for each group) as a function of the
>>>>>behavioral
>>>>>variable.
>>>>>Contrast [1 -1 0 0] then tests whether the groups differ at the
>>>>>intercept.
>>>>>Contrast [0 0 1 -1] tests whether the slopes differ.
>>>>>Those two contrasts are testing completely different things, so
>>>>>depending
>>>>>on what you are calling "group" vs. "interaction" images, the results
>>>>>you
>>>>>report are certainly possible.
>>>>>
>>>>>With that visual picture in mind, hopefully the model makes sense.
>>>>>
>>>>>cheers,
>>>>>-MH
>>>>>
>>>>>--
>>>>>Michael Harms, Ph.D.
>>>>>
>>>>>-----------------------------------------------------------
>>>>>Conte Center for the Neuroscience of Mental Disorders
>>>>>Washington University School of Medicine
>>>>>Department of Psychiatry, Box 8134
>>>>>660 South Euclid Ave. Tel: 314-747-6173
>>>>>St. Louis, MO 63110 Email: [log in to unmask]
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>On 7/29/13 6:16 PM, "Benjamin Philip" <[log in to unmask]> wrote:
>>>>>
>>>>>>Let me focus on the empirical reason, because it's much more
>>>>>>certain/convincing, even to me:
>>>>>>
>>>>>>I think it's incorrect because it doesn't hold up to the
>>>>>>reality-check
>>>>>>of
>>>>>>observing the two groups independently. In some areas the two
>>>>>>single-group images show drastically different z-statistic values
>>>>>>(e.g.
>>>>>>at X=61, Y=50, Z=68, Patient = 16.9, Ctl = 7.5), yet the interaction
>>>>>>image is not significant (interaction zstat=1.4). Conversely, there
>>>>>>are
>>>>>>areas where the two single-group images have nearly identical values
>>>>>>(e.g. 29/52/68, Patient = 23.6, Ctl = 23.1) yet the interaction image
>>>>>>is
>>>>>>significant (interaction zstat = 7.7).
>>>>>>
>>>>>>Whatever interaction effect that model produces, it isn't (P*b) -
>>>>>>(C*b).
>>>>>>
>>>>>>Files are at https://www.dropbox.com/sh/jajnm7gjnmfa615/ASA5he3gcg .
>>>>>>In
>>>>>>there you can find .png files for a quick-and-dirty show, and nifti
>>>>>>files
>>>>>>to demonstrate this at the voxel of your choice.
>>>>>>
>>>>>>Thanks,
>>>>>>-Benjamin Philip
>>>>>>
>>>>>>On Mon, 29 Jul 2013 18:11:28 +0000, Harms, Michael <[log in to unmask]>
>>>>>>wrote:
>>>>>>
>>>>>>>Hi Benjamin,
>>>>>>>The model that you need is the interaction one that you noted:
>>>>>>>http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM#Two_Groups_with_continuous
>>>>>>>_c
>>>>>>>ov
>>>>>>>a
>>>>>>>ri
>>>>>>>ate_interaction
>>>>>>>
>>>>>>>
>>>>>>>Why are you saying that it isn't correct?
>>>>>>>
>>>>>>>You can't look for an interaction between groups unless your model
>>>>>>>includes separate Behavioral EVs for each group.
>>>>>>>
>>>>>>>cheers,
>>>>>>>-MH
>>>>>>>
>>>>>>>--
>>>>>>>Michael Harms, Ph.D.
>>>>>>>
>>>>>>>-----------------------------------------------------------
>>>>>>>Conte Center for the Neuroscience of Mental Disorders
>>>>>>>Washington University School of Medicine
>>>>>>>Department of Psychiatry, Box 8134
>>>>>>>660 South Euclid Ave. Tel: 314-747-6173
>>>>>>>St. Louis, MO 63110 Email: [log in to unmask]
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>On 7/29/13 1:03 PM, "Benjamin Philip" <[log in to unmask]> wrote:
>>>>>>>
>>>>>>>>I'm having trouble organizing a FEAT third-level analysis
>>>>>>>>correctly.
>>>>>>>> I
>>>>>>>>have 2 groups, and a behavioral measurement for each participant.
>>>>>>>>What
>>>>>>>>I
>>>>>>>>really want to see is "Behavior-correlated activity in patients"
>>>>>>>>minus
>>>>>>>>"Behavior-correlated activity in controls". (P*b) - (C*b).
>>>>>>>>
>>>>>>>>I tried the interaction model suggested at
>>>>>>>>http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM#Two_Groups_with_continuou
>>>>>>>>s_
>>>>>>>>co
>>>>>>>>v
>>>>>>>>ar
>>>>>>>>iate_interaction but it's not addressing the correct question.
>>>>>>>>Theoretically I say this because we're looking for a subtraction,
>>>>>>>>not
>>>>>>>>an
>>>>>>>>interaction. More convincingly/clear-to-express, it's empirically
>>>>>>>>the
>>>>>>>>wrong model, because it produces results wildly different from what
>>>>>>>>we
>>>>>>>>see comparing (P*b) and (C*b) by eye.
>>>>>>>>
>>>>>>>>I've also tried a contrast of [1 -1 1] on the EVs "Patient,
>>>>>>>>Control,
>>>>>>>>Behavior" - i.e. like this oversimplified version:
>>>>>>>>Pat Ctl Bhvr
>>>>>>>> 1 0 .4
>>>>>>>> 1 0 -.2
>>>>>>>> 0 1 -.3
>>>>>>>> 0 1 .1
>>>>>>>>...If I do that, [1 -1 1] looks pleasingly different from [-1 1 1],
>>>>>>>>but
>>>>>>>>something is deeply wrong with this modeling: [1 -1 1] and [1 -1
>>>>>>>>-1]
>>>>>>>>and
>>>>>>>>even [1 -1 0] look nearly identical. The same areas can't be both
>>>>>>>>behavior-correlated and behavior-anticorrelated, so I'm doing
>>>>>>>>something
>>>>>>>>wrong. [1 1 -1] and [1 1 1] also look near-identical, but at least
>>>>>>>>[0
>>>>>>>>0
>>>>>>>>1] and [0 0 -1] show different areas.
>>>>>>>>
>>>>>>>>Any suggestions for how to implement (P*b) - (C*b)?
>>>>>>>>
>>>>>>>>Thanks,
>>>>>>>>
>>>>>>>>-Benjamin Philip
>>>>>>>
>>>>>>>
>>>>>>>________________________________
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>>>>>>>you are not the intended recipient, be advised that any unauthorized
>>>>>>>use, disclosure, copying or the taking of any action in reliance on
>>>>>>>the
>>>>>>>contents of this information is strictly prohibited. If you have
>>>>>>>received this email in error, please immediately notify the sender
>>>>>>>via
>>>>>>>telephone or return mail.
>>>>>
>>>>
>>>>
>>>>________________________________
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>>>>Healthcare Information or other information of a sensitive nature. If
>>>>you are not the intended recipient, be advised that any unauthorized
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>>>>contents of this information is strictly prohibited. If you have
>>>>received this email in error, please immediately notify the sender via
>>>>telephone or return mail.
>>
>>
>>________________________________
>>The materials in this message are private and may contain Protected
>>Healthcare Information or other information of a sensitive nature. If
>>you are not the intended recipient, be advised that any unauthorized
>>use, disclosure, copying or the taking of any action in reliance on the
>>contents of this information is strictly prohibited. If you have
>>received this email in error, please immediately notify the sender via
>>telephone or return mail.
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