Dear Ian,

> i've a question about the use of correlated parametric regressors.
> if one has a covariate and two parametric regressors of that covariate,
> what is the effect of a correlation between the parametric measures?
> more specifically, i assume that as with standard regression, if these
> additional parametric variables are themselves correlated, there is no
magic
> bullet to segregate their effects.
Exactly

> that is, if both are entered into the
> regression simultaneously with the covariate, their linear dependence
> will cause them to in essence "null" one another out with respect to any
> predictive value of either in isolation.  in contrast, if they are entered
> hierarchically, then which ever is first will capture the lion's share of
> the variance, with the second appearing to have no predictive value.

> is this the correct interpretation and if so, does SPM enter the
parametrics
> simultaneously or heirarchically in the design matrix?

If you use the "parametric modulation" option in SPM, it models both (or
more depending on the expansion) regressors simultaneously, but the
parametric modulation (i.e interaction) should be orthogonal with respect to
the main effect as they are mean corrected before convolution.

The order of covariates in the design matrix is not important. If you have
say skin conductance and heart rate parameters and they are highly
correlated there is no obvious way to disentangle the two subcomponents.
This is a common problem and only solvable by experimental manipulation i.e.
you need to experimentally manipulate one parameter with respect to the
other to render them uncorrelated. Having said that, it also depends on the
degree of correlation between the parameters: the less they are correlated,
the more independent information they carry and the more differential
effects can be revealed by a correlational approach to brain activation.


-Christian

Dr. Christian Büchel
Neurologische Universitätsklinik, Haus B
Universitäts-Krankenhaus Eppendorf
Martinistr. 52
D-20246 Hamburg
Germany
Tel.: +49-40-42803-4726  Fax.: +49-40-42803-9955
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www.uke.uni-hamburg.de/kliniken/neurologie/pages/mitarbeiter/buechel_c.htm