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Subject:

Re: Design model and contrasts

From:

[log in to unmask] (Jesper Andersson)

Reply-To:

[log in to unmask] (Jesper Andersson)

Date:

Mon, 3 Jan 2000 15:18:23 GMT

Content-Type:

text/plain

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text/plain (86 lines)

 
Dear Jason,
 
> 
> I have a question. I will start with explaining what I have and what I
> know and then follow with what I would like to know.
> 
> First:
>       The fmri experiment consists of simple on-off paradigms.
>       off (32s) on (32s) off(32s) on(32s) off(32s)
>       We are using SPM99b.
 
>From what you write below I assume you have several (>1) sessions
identical to this ones.
 
> 
>  Second:
>       The design matrix can be modelled with this session containing one
> or two conditions. I realize that modelling on and off seperately is
> redundant, and the degrees of freedom are slightly different between the
> two models. 
> 
>  I accept that the following is true: 
> One session
>       one condition model with a contrast=[1] is equal to two condition
> model with a contrast=[-1 1] (-1 -> off and 1 -> on).
>       likewise [-1] is equal to [1 -1]. 
>
 
If by a "two condition model" you mean one where baseline is
explicitly modelled, yes.
 
> Two sessions
>        (each with the above on-off paradigm) I accept the following to
> be true:
>       one condition model with a contrast=[-1 1] is the same as the two
> condition model with contrast=[1 -1 -1 1] ( 1 -> session1 off, -1
> ->session1 on, -1 -> session2 off, 1 -> session2 on)
> 
> Third
>       My question.
>       With one session, on and off modelled as seperate conditions, what
> does the contrast=[0 1] (0-> off, 1-> on) show?
>
 
I am afraid it doesnt mean very much, and had it been PET you
shouldn't be able to enter that contrast into the contrast manager.
What you have is two vectors (columns of your design matrix) that are
very close to colinear, but because of the convolution with the HRF
not completely. Had they been completely colinear their sum would
have been identical to the session effects (constant) column and the
parameter estimate associated with e.g. the second column (as in your
contrast above) would have been roughly half the difference between
on and off, PLUS an unknown part of the "baseline" activity.
When you enter the sensible contrast [-1 1] that problem dissapears 
since that linear combination of the parameter estimates would have 
been -1*(half the difference between off and on + unknown part) + 
1*(half the difference between on and off + unknown (but identical) 
part). Hence, the unknown contribution from the "baseline" activity
cancels out.
In your case (fMRI) the vectors will not be exactly colinear (but I am sure
you will find a correlation of ~0.98-0.99) and you will be allowed to
enter the contrast into the contrast manager. However, the same concern 
as above still applies, i.e. your parameters will be very inefficiently
estimated and associated with a large standard deviation. My guess is 
that with the contrast [-1 1] you will see a nice SPM with high z-scores
in expected areas, whereas in the [0 1] contrast you will see very little.
 
 
> Also with two sessions, on and off modelled as seperate conditions
> what doe sthe contrast=[0 -1 0 1] (0 ->session1 off, -1 ->session1 on, 0
> ->session2 off, 1 ->session2 on) show?
> 
 
If we call [0 1] for an "inefficient main effects of task" contrast,
we can call [0 -1 0 1] for an "inefficient task-by-session
interaction" contrast.
 
> 
>       I hope that I explained myself well,
>       Thank you,
>               Jason.
> 
 
                                        Good luck Jesper

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