Dear Roland
(> 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 ?
>
Yes - see email for entering more than one modulator in SPM99/SPM2:
http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind04&L=SPM&P=R202727&I=-3 - I
think this is mostly the same in SPM5 but haven't used it myself (with a
minor difference, see next link).
The only catch is that that each modulating variable is orthogonalised with
respect to the preceding ones (this is in addition to how you calculate the
interaction vector) - see
http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=ind0602&L=SPM&P=R53910&I=-3
This is important as it affects the priority with which variance is
attributed to your different modulating variables - you will have to pick
one main effect to be first, another second, and the interaction
(presumably) last. Unless there is something I'm missing (anyone?)
I think Rik Henson faces/lag example analysis does something like this so do
recommend you have a look.
HTH, Alexa
>
> -----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
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