Dear Karl,

Thanks very much for your speedy and extensive reply!! It really  
helped clarify things!

Best wishes,
Sophie


> Dear Sophie,
>
>> I am interested in the use of psychophysiological interactions and
>> have read your 1997 paper in NeuroImage (Psychophysiological and
>> Modulatory Interactions in Neuroimaging) and I have a question or two
>> that I am wondering whether you can help me with. I understand that
>> you are very busy and that you may be unable to respond to this
>> e-mail, but thought that since my question relates specifically to
>> your paper,you would be the best person to ask about it.
>>
>> I have been reading around the idea of using PPI as a method of
>> effective connectivity when the physiological activity of a number of
>> regions (say B, C and D) are entered into the model, and as a method
>> of establishing ?contribution? of region A to region B when only a
>> single or a couple of regions are entered into the model. I see some
>> people refer to PPI analyses as a measure of functional connectivity,
>> and others refer to it as effective connectivity.
>



> I have to confess that I am ambivalent about the status of PPI as a  
> measure of functional
> or effective connectivity. According to the definition of functional  
> connectivity (a significant
> statistical dependence between dynamics in two areas), one can  
> regard a PPIs as testing
> for functional connectivity because they are based on a significant  
> interaction. On the other hand,
> this significance is based on rejecting the null hypothesis that the  
> parameter of the underlying
> PPI model is non-zero.  This parameter reflects the unique  
> contribution of the interaction to
> the observed responses in the target area; and could be interpreted  
> as effective connectivity;
> i.e., the influence of one area on another under some model.
>


>
>> If I am correct, I think that you are saying the following in your
>> paper: when a number of different areas are entered into the model
>> (B,C, D), the parameter estimates can be treated almost like
>> connectivity strengths and so this resembles effectve connectivity,
>> whereas when only one (B) or two (B,C)  areas are entered into the
>> model, these parameter estimates are less like connectivity strengths
>> because one ignores other areas (say D, etc) that may be explaining
>> variance in the region of interest (A), and so this is refered to as
>> 'contribution'. Is my understanding correct?
>


> Yes, although the notion of a contribution does not rest on the  
> number of areas; it is simply the
> contribution of one area to the variance in another that cannot be  
> explained by other
> contributions.  Clearly, the latter qualification depends on there  
> being other areas but one
> area can still contribute to another. The use of the term  
> contribution reflects the nature of the
> general linear model of effective connectivity used in PPI and is  
> closely related to the path
> coefficients (of moderator variables) in structural equation (and  
> other linear regression) models
> of effective connectivity. It also appears in contribution analyses.
>
>
>> So far, I have used PPI to look for changes in the contribution of one
>> region to another, including no other regions.
>>
>> My question is this. When there is only one area included in the model
>> (my seed area is the anterior temporal lobe), and I compare the
>> significant interaction effects seen in one condition to those in
>> another, how is this different to comparing two correlation analyses?
>> Isn?t a simple regression including only one predictor region
>> (interacting with condition) and the outcome ROI just the same as
>> performing a correlation analysis between the two areas under a given
>> condition?   The only reason that I ask, is because of a sentence in
>> the discussion of the 1997 paper that says:
>>
>> ?Note that both these analyses included the effects from many possible
>> sources of input and were framed in terms of effective connectivity.
>> In this paper the effects modelled derive from only one region and are
>> framed in terms of contribution. The analysis presented in this paper
>> does not constitute an analysis of effective connectivity for this
>> reason (but see below)..............However, in relation to
>> psychophysiological interactions, it should be noted that a test for a
>> change in regression slope does not constitute a test for a change in
>> correlation, even in the context of a single explanatory region.?
>
>> So putting only one region into the model, you frame in terms of
>> contribution rather than effective connectivity, but this
>> ?contribution? is not the same as functional connectivity, because
>> testing for a change in correlation is not the same as testing for a
>> change in regression. Please could you clarify for me how, in the case
>> of regression with a single explanatory variable, the test is
>> different for a change in regression slope to the change in correlation?
>
>


> There is a fundamental difference between a PPI (even with one area)  
> and tests for a
> change in correlation. This is because the correlation coefficient  
> is not an estimate of
> connectivity - it is a statistic that is a function of the estimate  
> (i.e., regression coefficient)
> and its standard error. This means that if the correlation  
> coefficient changes, one does
> not know whether the parameter (effective connectivity) has changed  
> or whether the
> noise level has changed.
>


> Generally speaking, it is bad practice to compare statistics (one  
> uses statistics to compare).
> An unfortunate but common violation of good practice is to compare  
> correlation
> coefficients with Fishers Z-transform. This is not a test for a  
> change in coupling
> but  tests for the change in the significance of a coupling, where  
> the coupling per se may
> or not have changed
>
>> Along similar lines, I have read that the PPI provides directional
>> information- i.e regressing area A x psych condition onto area B,
>> isn?t the same as regression area B x psych condition onto area A.
>> Please can you elaborate on how this is the case?
>


> Yes, the interaction term breaks the symmetry.  This can be seen  
> from a number of perspectives;
> for example, assume that B = A x psych.  This would give a very  
> strong PPI when regressing
> A x psych on B. However, the reverse regression B x psych on A would  
> give a very different
> result because B x psych = A x psych x psych, which cannot be equal to A.
>
> I hope this helps.
>
> With very best wishes,
>
> Karl
>
>