Hi Jonathan
> Dear John,
> I have a design matrix with 3 parametric regressors PA, PB and PC (in
>> that order)
>>
>> Now, i create a second DM with the following regressors PA,PB,PD,PE.
>>
>> Whereas the results for PA remain the same, the results for PB change.
>> One reason could be that PE and PB are somehow correlated;
>> however, I thought that the correlation would have an effect on PE and
>> not on PB, given that PB appears first in the DM
>>
>> Could somebody explain why results from PB in the first DM are different
>> from results of PB in the second DM?
>
> Most likely you are right - the correlation of PB with other
> regressors (PC vs. PD/PE) is not the same, which will give you
> different results.
> (Also it's important to know what you mean by "results" - the beta
> estimate for PB, or the t statistic from a contrast on PB? The
> inclusion of additional regressors may not only affect the estimate of
> the PB beta, but also the error term, which would give you a different
> t statistic image.)
given the orthogonalization, this has to be the same Beta value, but the
results will differ since residuals will be smaller
>
> You can look at the correlation between columns in your design matrix
> by clicking the "review" button, and then under the "design" menu
> select "design orthogonality".
> Alternatively you can look at the modulators from your design matrix
> as entered, which is stored in SPM.xX.X. Something like this:
> load SPM
> PB = SPM.xX.X(:,2);
> PC = SPM.xX.X(:,3);
> [r, p] = corrcoef(PB, PC);
> plot(PB, PC, 'o');
remember that corrcoef is the mean centered correlation whereas in spm
that is just the cos(angle) between regressors (not such a big
difference but worthwhile remembering - cos(angle) = corr only is the
vectors are normalized)
Cyril
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