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
|