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_continuous_
>>>>>>>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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>>>>>>the
>>>>>>contents of this information is strictly prohibited. If you have
>>>>>>received this email in error, please immediately notify the sender via
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>>>>
>>>
>>>
>>>________________________________
>>>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
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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
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>
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>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.