When there is more than one covariate in the design matrix, the permutation
algorithm would proceed by permuting the rows of the matrix, keeping the
predictor variables together during the permutation. In case of a nuisance
covariate Z, it could influence the linear association with the covariate of
interest X since the observed variable Y is adjusted for the nuisance
covariate Z. However, doesn't this simply mean that the inference on the
association between X and Y is conditional on the observed nuisance
covariate Z? My argument here is that the considerations raised by Dr
Hayasaka have an impact on the type of inference that can be drawn that has
very limited importance in practice.
I realize that my contribution here may be perceived as rather nitpicky, and
I apologize for this. However, I believe permutation methods to have a real
edge in neuroimaging over parametric methods. My concern is that portraying
permutation methods as not applicable in the presence of a covariate applies
unecessarily high standards. In contrast, I think that use of permutation
methods by experimenters should be encouraged.
R. Viviani
Dept. of Psychiatry
University of Ulm, Germany
----- Original Message -----
From: "Satoru Hayasaka" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, July 23, 2007 8:11 PM
Subject: Re: SnPM multiple regression.
Dear Gracian (and SnPM users),
> I'm performing a regression study with Statisticl non-Parametric
> Mapping (SnPM5 for SPM5 package). I'm wonder if is possible to
> design a model with more than one covariate of interest (i.e.
> perform a multiple regression model).
Unfortunately, the answer is "No". But there is quite a bit of debate
whether it is appropriate to include multiple covariates in a regression
analysis in SnPM. As you may know, SnPM randomly shuffles observations
to generate the probability distribution for a statistical test,
assuming that there is no association between your image data and the
covariate. However this assumption may or may not hold when you have two
or more covariates, because the association between the images Y and the
covariate X could be influenced by an additional covariate Z in your
model. That is the reason why SnPM doesn't have such a study design.
-Satoru
Satoru Hayasaka PhD ----------
Assistant Professor, Public Health Sciences & Radiology
Wake Forest University School of Medicine
(ph) +1-336-716-8504 / (fax) +1-336-716-0798
(email) shayasak _at_ wfubmc _dot_ edu
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