Zhang -
I think what you have noticed is that, if you model
P levels of a parametric factor separately, a linearly-
weighted contrast doesn't necessarily pick out only
linear patterns across each level.
If however you modelled your P levels with a single
column, with values of -2 for 0ms SOA trial, -1 for
50ms SOA trial, etc, in your case, then a [1] contrast
in this model (or more precisely, a [1 0] contrast,
since you need to model to mean as well, or a [0 1 0]
contrast if you are modelling events together with a
linear parametric modulation) will tend to pick out
only true linear modulations by SOA.
This is because the first model above is powerful enough
to fit any patterns across the P levels, so that the
residual error will tend to be small, and hence contrasts
that show a rough increase with SOA will tend to be significant.
The second model however is more constrained(fewer df's) and
patterns that diverge from a linear fit will result in a larger residual error and hence are less likely to be significant.
Rik
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DR RICHARD HENSON
MRC Cognition & Brain Sciences Unit
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URL: http://www.mrc-cbu.cam.ac.uk/~rik.henson
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----- Original Message -----
From: "Zhang Peng" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, April 05, 2005 4:54 PM
Subject: [SPM] Parametric contrasts questions
> The issue is general, but a specific example will
> probably help: my conditions are audio-visual stimuli,
> with each condition being a different SOA between
> the auditory stimulus and the visual stimulus,
> one column in the design matrix for each SOA-type.
>
> Suppose I'm doing a contrast to find areas whose activity
> increases with increasing SOA.
>
> Then the contrast has, say,
> -2 for the 0ms-SOA cols
> -1 for the 50ms-SOA cols
> 0 for the 100ms-SOA cols
> 1 for the 150ms-SOA cols
> 2 for the 200ms-SOA cols
> etc.
>
> The problem is that this contrast doesn't only find areas
> whose activity scales linearly with SOA. It finds any area
> that is more active on average for the cols that have positive
> coefficients than for the cols that have negative coefficients.
>
> e.g. if the beta scores in a given voxel
> for the conditions [ 0ms 50ms 100ms 150ms 200ms ]
> are [ 1 2 3 4 5 ], i.e. if neural activity really does scale
> linearly with increasing SOA, as is desired, then
> that voxel will give a good contrast score.
> However, we'll get an equally big contrast score
> if the activity doesn't match the linear-increasing
> form of the contrast vector, e.g. if the beta scores
> for the conditions [ 0ms 50ms 100ms 150ms 200ms ] are [ 0 0 0 0 5 ].
>
> sum( [ -2 -1 0 1 2 ] .* [ 1 2 3 4 5 ] ) = 10 but also
> sum( [ -2 -1 0 1 2 ] .* [ 0 0 0 0 5 ] ) = 10,
> so both show up as equally significant, even though the first
> one is the better match to our parametric contrast,
> coming from a voxel whose activity really does increase
> with increasing SOA, whereas the second voxel example
> just gives a big kick of activity for the longest SOA only.
>
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