Dear Priyantha,

I noticed no-one else had answered this so I thought I'd give it a quick go.


  1.      I know that there are 4 different options to model the response
  function in the SPM99b.. namely... Fixed box car, Discrete Cosine set etc.
  I noticed that the first two, DCS and the mean and expo. decay
  models additional regressors,  where as box car and half sine functions do
  not. How does one select what response function is the best for a particular
  paradigm?I realize that the fancy stuff like DCS etc are more
  suitable for efMRI, but for the usual blocked designs,  what is best?

    None of the suggested options are always the 'best' model to use: they each
depend on the form of the neuronal response to your paradigm. The 'box-car'
function assumes that an immediate, tonic response results from your behavioural
intervention (i.e. your experimental task/stimulation), and ceases more-or-less
immediately when it does (hence its shape and name). However, although this may
hold for the primary sensory cortices, other models may be more appropriate for
different spatial locations and paradigms. For example, use of the half-sine
regressor as your stiumulus waveform produces a smoother boxcar with a gradual
rise and decay, and the mean and exponetial decay option allows you to model
hemodynamic
responses which decay over the period of the task. This can be understood in the
context of a neuronal response which undergoes habituation to repeated
stimulation, for example. If you play with the 'fMRI design' button, and review
the design matrices afterwards, you can see these changes in detail, and also
what they look like after convolution with the hrf.
To sum up, each regressor is essentially asking a different question - you have
to choose which one is appropriate for you.


  2.      I also noticed that depending on modelling intrincic correlations
  of the time series and many other manipulations that one does,the
  effective DF for a given contrast varies, although the number of
  parameters estimated in the model is the same in both situations ( ie AR+
  or not etc..). How is this possible and what does it mean in terms of the
  outcome of the analysis?

This is an example of where fMRI differs from PET. In PET, each scan is treated
as an independent observation.
In fMRI the presence of temporal autocorrelations violates this assumption
(basically, each scan is part of a timeseries, and so the correlation between
successive terms is not zero). The approach within SPM to overcome these
difficulties is to use 'temporal smoothing (old school term)' or 'low-pass
filtering(new school term)', and, by extension, the use of first-order
auto-regressive models (the AR(1) option) to overcome this problem. As the
degrees of freedom are affected by the number of independent observations in the
data, and changing the autocorrelation strcuture (by
filtering/smoothing/whatever) will effect this, I'm sure you can see how your
dfs come to be different.


  3.      In general, how does one asses the goodness of the fit in a
  particular model for any given paradigm? Having modelled the data set in
  many different possible ways, what factors should favour the selection of
  a particular model and the emanating SPM t maps over the others?


This is known as a 'model selection' problem, and basically boils down to a kind
of Hobson's choice: should I attempt to include every component of interest in
my model, and so model the experimental variance well but lose dfs - or vice
versa? The usual way this problem is dealt with is by either forward or backward
selection: taking a very sparse model and adding regressors to it until the
extra variance explained by the regressors added is not significant (forward
selection), or starting with a megamodel and assessing the effects of removing
regressors,  using an extra sum-of-squares F statistic to assess significance in
both cases. This topic is well detailed in 'the book' (Human Brain Function, on
pages 78-80) by Andrew. A good recent example of model selection is by Aguirre
and colleagues in their recent paper in Neuroimage on the inclusion of
subject-specific regressors in a study examining the variability
of hemodynamic responses, although they employed a partial F test, not an ESS F
(hope I remember that right!).

Hope all of the above is of some use

Best

Dave McG.

 Thank you so much,

 Priyantha Herath, MBBS

  Division of Human Brain Research,               tel:     +46 (0)8 728 7298
  Department of Neuroscience,                              +46 (0)8 728 7297
  Karolinska Institute,
  S 171 77 Stockholm,                             fax:      +46  8 309045
  Sweden.



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