Dear Rebecca and Geraint,
> |c) For future reference, does the logic extend to a design with n
> |conditions where n>2, ie: does one always specify n-1 conditions on
> |the basis that the nth is implicitly completely specified?
>
> Hmmm...I always wondered about this too but can't figure it out in my
> head. Is it that some linear combination of the parameter estimates for
> the n-1 conditions can specify the nth? Someone else will have to answer
> this one...
It depends on the form of responses modelled. Geraint is absolutely
right in that when using box-car regressors the nth condition can
always be modelled by some linear combination of the other conditions
and the constant term. Therefore, in this situation, explicitly
modelling the nth condition is unnecessary. However for every model
apart from a box-car (e.g. sine waves or multiple basis functions) this
is not the case and omitting the nth condition is like forcing it to be
modelled in terms of constant activity. This may be appropriate for
null events and rest but in control conditions, where you have
adaptation, you may want to model the nth condition explicitly to give
a slightly better model.
Very best wishes - Karl
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