Dear Alexa,

Thanks again for responding to my questions ..
I just wanted to make sure I understand your answers correctly:

(> Another question, what if in an fMRI study using words as stimuli I
> wanted to model the interaction of two stimulus parameters (say word
> frequency x imageability, with one value per stimulus). Could I do the
> same thing and just enter the product of both values for each stimulus
> as a covariate to be convolved with stimulus-specific HRF at the first
> level ?

Here you are talking about a parametric modulation - at the 1st level -
this
is easy to do using the GUI, just enter your two variables as parmatric
modulations. Check out the SPM5 manual and analyses of example datasets
as
well.)

>> Can I enter the two variables as two parametric regressors per
stimulus >> at the first level and then enter the product of both
variables as a the
>> parametric regressor to model the interaction ?

Thanks again for your help !
Roland
 

Roland Zahn, Dr. med.
NIH / NINDS
Cognitive Neuroscience Section
Building 10, 5C206
10 Center Drive, MSC 1440
Bethesda, MD 20892-1440
Tel.: (+1)-301-402-6392
Fax.: (+1)-301-480-2909

 

-----Original Message-----
From: Alexa Morcom [mailto:[log in to unmask]]
Sent: Friday, September 29, 2006 3:49 AM
To: [log in to unmask]
Subject: Re: [SPM] clarification of interactions modelled on second
level

Dear Roland

I hope you don't mind me copying this one to the list too

> Thanks for immediately responding to my question and referring to the
> chapter, which I looked at and had the impression it talks about
> interaction of categorical factors, which I think in my case is not
> applicable, because I want to test interaction of effects of two
> stimulus parameters in an fMRI study.
>
You're right, the chapter does talk about categorical designs, perhaps
someone can recommend a more general book on the GLM? (Google and the
StatSoft website are quite useful too!)
>
> You mention that if one wants to model the interaction of two
parametric
> factors (I suppose for subject based factors), one would have to add a
> covariate column which represents a product of two continous variables
> over subjects into the ANOVA at the second level.
>
> In order to do that, could I just multiply the two values for each
> variable in each subject and then enter the product value as a
> covariate ?
>
This sounds like a covariate over subjects. Are you using SPM5? If so,
you
can enter a covariate in a full-factorial ANOVA model and then specify
which
factor it interacts with. It will then divide up the covariate so it has
n
columns where n is the number of levels of your factor. (Check the mean
centring matches this)

If you have a design with purely continuous variables and these interact
with one another not with categorical variables the usual thing to use
is a
multiple regression design, but you would have to make the interactions
yourself by multiplying values.

...I believe these need to be mean centred first (by hand - easy in
matlab)
and then again in the model but someone please correct me if I am wrong.


> Another question, what if in an fMRI study using words as stimuli I
> wanted to model the interaction of two stimulus parameters (say word
> frequency x imageability, with one value per stimulus). Could I do the
> same thing and just enter the product of both values for each stimulus
> as a covariate to be convolved with stimulus-specific HRF at the first
> level ?

Here you are talking about a parametric modulation - at the 1st level -
this
is easy to do using the GUI, just enter your two variables as parmatric
modulations. Check out the SPM5 manual and analyses of example datasets
as
well.

Good luck

Alexa



>
>
> This would be a really great thing !
>
> Thanks for your advice !!
>
> Best,
> Roland
>
>
>
>
> Roland Zahn, Dr. med.
> NIH / NINDS
> Cognitive Neuroscience Section
> Building 10, 5C206
> 10 Center Drive, MSC 1440
> Bethesda, MD 20892-1440
> Tel.: (+1)-301-402-6392
> Fax.: (+1)-301-480-2909
>
>
>
> -----Original Message-----
> From: Alexa Morcom [mailto:[log in to unmask]]
> Sent: Thursday, September 28, 2006 4:06 AM
> To: Zahn, Roland (NIH/NINDS) [V]; [log in to unmask]
> Subject: RE: [SPM] clarification of interactions modelled on second
> level
>
> As far as I understand it an interaction is just an effect that
depends
> on
> another effect, and in mathematical terms it is as you say a product
of
> two
> predictors
>
> In general, 1 -1 tests a difference between two parameter estimates or
> existing contrasts, not an interaction. For categorical predictors an
> interaction is not as a general rule modelled by 1 -1. SPM models are
> also
> complex in that a 2-stage procedure is used and at the 2nd level
> different
> kinds of things may be compared.
>
> I recommend Rik's & Will's ANOVA note
> http://www.fil.ion.ucl.ac.uk/~wpenny/publications/rik_anova.pdf
>
> Perhaps some examples will help
> - If your 1st level contrasts are 1 0 for 2 conditions against some
> baseline, the 2nd level contrast 1 -1 tests for a difference in their
> difference from baseline. This is in a mathematical sense an
interaction
> but
> may not be the one you are interested in
> - It's possible to create 1st level contrasts that are already
> differences
> between conditions (in a 'partitioned error' 2nd level model), and
then
> test
> for an interaction, but the contrast for this is not in general 1 -1
> (although is for a 2 sample t-test; see the technical note)
> - If your first level contrasts already represent interactions (e.g. 1
> -1 -1
> 1 for 2 factors), then a main effect at the second level (1 0 as in a
> one
> sample t-test) will give you your interaction effect
>
> These 1- or 2-stage 'difference in differences' procedures work for
> categorical predictors that but for continuous predictors I think you
> just
> have to multiply - in SPM it is done at the first level in a PPI or
> physiophysiological interaction and could be done by adding a
covariate
> column into an SPM5 ANOVA model which represents a product of two
> continuous
> variables over subjects.
>
> HTH - someone else may be able to add something pithy!
>
> Alexa
>
>
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]
> On
> Behalf Of Roland Zahn
> Sent: 28 September 2006 00:04
> To: [log in to unmask]
> Subject: [SPM] clarification of interactions modelled on second level
>
> Dear SPM experts,
>
> I have a question regarding the use of the term "interaction" when
SPM5
> sets up a factorial model on the second level.
>
> As I have understood interactions between two factors are modelled by
> entering say 1 for factor 1 and -1 for factor 2 into the contrast
> manager.
>
> But how does this relate to the interaction terms used in a multiple
> regression model when one uses a statistical software (e.g. SPSS).
>
> I always thought the interaction term would normally be a
multiplication
>
> of two predictors, which have to be estimated by a least square
solution
>
> in the multiple regression model.
>
> What I do, when I enter 1 -1 for factor 1 and factor 2 respectively
into
>
> the contrast manager in SPM, however, is to look for inverse partial
or
>
> adjusted effects of the two factors (since as I have understood SPM
> always
> yields partial effects adjusted for everything else in the model),
> correct ?
>
> I don't quite understand how both ways of modelling an interaction
> relates
> to one another, or did I get the way how to model interactions in SPM
> wrong ?
>
> Can anybody help to dissolve my confusion ?
>
> I must have an error of understanding somewhere ....
>
>
> Thanks a lot for any hint !!
>
> Best,
> Roland
>
>
>
> Roland Zahn, Dr. med.
> NIH / NINDS
> Cognitive Neuroscience Section
> Building 10, 5C206
> 10 Center Drive, MSC 1440
> Bethesda, MD 20892-1440
> Tel.: (+1)-301-402-6392
> Fax.: (+1)-301-480-2909