Dear Karl,

Thanks for the clear and concise reply.  I have now conducted a multi-group
conditions and covariates analysis as you suggested:

>> Alternatively would one use 2 covariates ?  Each covariate consisting of
>> the mean centered values for a single group with 0 padding for the
>> subjects in the other group, essentially what you get when you specify a
>> group x covariate interaction  The effect of the covariate for group 1
>> alone would be tested with the contrast 0 0 0 0 1 0 ( (Group 1, Group 2,
>> Condition 1, Condition 2, Covariate1, Covariate 2)  and the interaction
>> across groups tested with the contrast 0 0 0 0 1 -1 ?

>Exactly.


First, I have noticed that there are clear differences in the SPM if the
effect of the covariate alone for a single group is tested in a
multi-subject: conditions and covariate design (e.g. 0 0 1) and the
multi-group design (e.g. group 1 - 0 0 0 0 1 0).  I would like to know which
design is more appropriate for testing the effects within a single group.
My bias is that one would use the single group design.   In a simple linear
regression between the change in a pixel value across conditions and a
change in the covariate, adding a second group of subjects with all 0s for
the covariate gives a different correlation confident than a regression with
just the subjects from a single group.  I suspect the same logic holds for
assessing the effect of the condition within a single group.  Of course, the
multi-group design is needed to test for interactions.

Second, when mean-centering the covariate for entry in a multi-group design
should  0 padding entered for the covariate for the second group be taken
into account when calculating the mean ?  I would think not because then the
covariate values for the second group would have a non-zero value have
subjecting the mean.

Third, in a single group model, Andrew Holmes has indicated that one can use
the standard formula to convert t-values to r-values (correlation
coeffients), which I have confirmed empirically.  However, if there is more
than one covariate then one has to use a more complicated procedure that
takes the partial correlation and the larger number of degrees of freedom in
the error term into account.  Does this latter case hold for the multi-group
model where one has created two separate columns in the design matrix for
the covariate, one for each group ? More directly, how would one derive the
correlation confident from the t-value for a contrast of the covariate
within a single group (e.g. 0 0 0 0 1 0).

Third, would the contrast 0 0 0 0 1 1 in the multi-group model be a test of
the effect of the covariate collapsed across all subjects disregarding group
membership ?

Thanks.



sg

( Note new e-mail address:
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====================================
Steven Grant, Ph.D.
Cognitive Neuroscience of Addiction Program
Clinical Neurobiology Unit
Div. Treatment Research & Development
National Institute on Drug Abuse
Room 4-4238
6001 Executive Blvd
Bethesda, MD 20892 
301 443-4877 (voice)  443-6814 (fax)



-----Original Message-----
From: [log in to unmask] [mailto:[log in to unmask]]
Sent: Wednesday, June 28, 2000 7:18 AM
To: Grant, Steven (NIDA); [log in to unmask]
Cc: [log in to unmask]
Subject: Multi-Group Correlations


Dear Steve and Leann,

> Given 2 conditions,  1 scan/condition, 1 covariate obtained at each scan,
> mean-centered covariate with proportional global scaling.  A condition &
> covariate design with a contrast 0 0 1 is equivalent to correlation
> between the change in covariate and the change in the scans.

Indeed or more precisely the partial correlation between the covariate
and scan-by-scan changes having accounted for the condition-specific
activations.

> Can this approach be generalized to a multi-group design ?  If there are 2
> groups and 2 conditions, with 1 scan for each subject under each
> condition, and a single covariate collected during each scan, then would
> one specify 1 or 2 covariates.

I would specify two, each with a group-centered covariate.  This would
allow you to look for differences in the partial correlation with the
contrast [0 0 0 0 1 -1].  i.e. models group x covariate interactions.

> If only one covariate is specified,  would one test for a covariate effect
> in group 1 alone with the contrast 1 0 0 0 1 (Group 1, Group 2, Condition
> 1, Condition 2, Covariate), and the group x covariate interaction with the
> contrast  1 -1 0 0 1 ? 

No. The interaction is not modeled with only one covariate.  This contrast
is simply the main effect of group plus the main effect of contrast.

> Alternatively would one use 2 covariates ?  Each covariate consisting of
> the mean centered values for a single group with 0 padding for the
> subjects in the other group, essentially what you get when you specify a
> group x covariate interation  The effect of the covariate for group 1
> alone would be tested with the contrast 0 0 0 0 1 0 ( (Group 1, Group 2,
> Condition 1, Condition 2, Covariate1, Covariate 2)  and the interaction
> across groups tested with the contrast 0 0 0 0 1 -1 ?

Exactly.


                              ---------------

> I have a very similar question to that posted by Steven Grant on June
> 9th.  I have two groups of subjects who, on prescreening, exhibited
> differential mood responses (one group positive scores, the other
> negative) to a drug.  So with 2 groups (positive and negative
> responders), 2 conditions (drug and placebo), 1 scan/subject under each
> condition, and 1 covariate (mood score) collected/scan, how would I go
> about determing whether rCMglu is affected by:
> 
> 1) prescreening mood scores both within and across groups

These are the simple and main effects of mood (or group) and would be
best addressed with a second-level analysis using the subject-effect
parameter estimate images (i.e. averaging over condotions for each
subject).

> 2) post drug scan mood scores both within and across groups
> and also whether:

This is a main effect of 'post scan mood score' within the post drug
level of the condition effect.  This is best analysed using a
condition-centered covariate ('post scan mood score') and testing for a
significant regression with 'drug'.

> 3) mean centering of the covariate is useful/necessary in these cases

Yes.  For (1) there is not covariate required.

> 4) mean should be computed within group or across all subjects

For (2) within condition.  There are other centering you could use to
look at different interactions. e.g. group-centered would allow you to
see if there was any interaction between prescreening and post scan
mood.

I hope this helps - Karl


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