Michael:

I agree that PPI is the wrong tool to disambiguate alternative directional influences between regions, but that doesn't mean we should hold it to a higher standard than other regression methods or that having a "biological" model is an invalid way of making hypotheses about directional influences. What appear to be statistically "proven" interpretations are also built on models whose interpretation can turn out to be ephemeral depending on your viewpoint. 

Please consider the experiment of flashing a checkerboard while measuring the brain's bold signal. To analyze this I could set up a boxcar function of the onsets of the checkerboard and analyze it using linear regression. I am sure that I would find highly correlated signal in V1 corresponding to the times the checkerboard was on. I think most people would generally agree that I had demonstrated that the flashing checkerboard had caused the corresponding activity in V1, i.e., the directional influence is from the checkerboard to V1. I probably wouldn't even get much argument if I claimed I had statistically proven this result (well perhaps from statisticians).

But have I really statistically proven this directional influence? What if instead I took signal from V1 and put it in the regression equation and looked at signals in the environment? I would bet that it would correlate with the flashing checkerboard and not other environmental signals such as scanner noise.  Could I now says this proves that V1 activity caused the flashing checkerboard? Most people would consider the statement ridiculous but it's only ridiculous  because everyone is willing to accept my biological model that visual stimuli cause V1 activity but not the alternative model that V1 activity causes visual stimuli in the environment. (However, if a researcher was from another planet where the beings had LCD projectors in their "eyes" perhaps both models would be equally valid. In that case I could not statistically prove, using regression, whether the flashing pattern caused brain activity or brain activity caused the flashing pattern, and regression would be the wrong tool to disambiguate these alternative models.)

Similarly, while I can't use PPI to disambiguate A->B or B->A, if I have a strong biological hypothesis that the influence is from A->B and PPI says a significant influence exists then it is not unreasonable for me to say that given my "strong" model and a statistically significant PPI result the direction of influence is from A->B.  Someone could of course claim that the influence was actually from B->A, but that is a different model. If I have no hypothesis about the direction then I would just say there was an influence but that it could be in either direction.

In any case, I think PPI is a good tool for looking at the presence of context dependent changes in activity between 2 or more regions. It's not a good tool to decide in the absence of a model what the direction of that influence is, but that's ok. I would use another tool such as DCM if I wanted to make a strong statement about the directional influences.

Thanks for the discussion.

Darren
 

On Sat, Jan 22, 2011 at 3:26 PM, Michael Harms <[log in to unmask]> wrote:

Perhaps it is a terminology thing, but what do you mean by "PPI allows
an inference about directionality because you have specified the
alternative model"?  In the context of statistical issues, I think that
the term "inference" should be reserved for true statistical inference
(i.e., "independent statistical statements" as you put it).  And what is
the "alternative model" -- all I see is a standard "null hypothesis" in
which you are testing the significance of the regressor against zero.
One can of course always make a biological argument favoring
interpretation of a particular causal direction in a given context, but
it is very important in my opinion to make clear that that is a
biologically motivated interpretation, and not a statistically proven
directional inference.

cheers,
-MH

On Sat, 2011-01-22 at 11:00 -0500, Darren Gitelman wrote:
> Michael
>
> On Sat, Jan 22, 2011 at 10:31 AM, Michael Harms
> <[log in to unmask]> wrote:
>
>         Hello Darren,
>         I'm confused by some aspects of your response.  You wrote that
>         Donald was
>         very correct in his responses, and Donald had written that you
>         basically
>         can't infer directionality from PPI because it a correlational
>         approach.
>         Donald's understanding is mine as well.  But your interspersed
>         comments
>         then seem to go on to say the opposite of that -- i.e., that
>         PPI does
>         allow inferences about directional coupling. While prior
>         knowledge may
>         permit arguments that certain directions are more
>         "plausible" (which
>         sounds like what was done in the Grabenhorst & Rolls article
>         you
>         mentioned), I don't see anything that allows you to make
>         STATISTICALLY
>         justified inferences about directionality, since the null
>         hypothesis is
>         simply that the interaction term is non-significant in the
>         presence of the
>         other regressors.
>
>         cheers,
>         -MH
>
> Exactly.  You cannot use PPI to make an independent "statistical"
> statement about the absolute direction of the influence, but you
> shouldn't let that trouble you. This is why I brought up the
> Grabenhorst and Rolls paper because they did a nice of showing how you
> can pick a seed (source) region but have an inference about the
> directionality that is actually target to source (prefrontal to
> orbitofrontal) rather than the canonical source to target. As I said,
> PPI allows an inference about directionality because you have
> specified the alternative model. Of course someone could disagree with
> your model but that's ok.
>
> I think as initially conceived or perhaps interpreted in the
> literature PPI was thought to confer a statement about absolute
> directionality, and this is not the case. It allows you to make a
> statement about the influences between regions and the response of
> that influence to task modulation, with the directionality being
> something you specify based on other information.
>
> Darren
>
>
>
>         > Dear  Andre
>         >
>         > I think Donald is very correct in his responses, further
>         comments below.
>         >
>         > On Fri, Jan 21, 2011 at 2:21 AM, Andre Szameitat
>         > <[log in to unmask]>wrote:
>         >
>         >> Dear Donald,
>         >> thanks a lot for your reply. However, I have follow-up
>         questions:
>         >>
>         >> >> 1) Can directionality be inferred or not?
>         >> > It hard to draw directionality because its a
>         correlational approach.
>         >> As far as I understood, it is not a correlational approach.
>         It is based
>         >> on a regression. While in correlation, the variables X and
>         Y can easily
>         >> be swapped, the regression coefficient (not its
>         significance though)
>         >> depends on whether X is regressed on Y or Y is regressed on
>         X. In other
>         >> words, regression is not symmetric.
>         >>
>         >> However, your opinion is what I thought so far as well. Do
>         you have
>         >> some  reference supporting your statement? Most other
>         people on this
>         >> list seem to be of the opinion that you can infer
>         directionality.
>         >>
>         >
>         >
>         > PPI is based on a regression, but, and this is a fundamental
>         point, it is
>         > a
>         > regression in which you have chosen the independent and
>         dependent
>         > variables,
>         > and they could equally well have been switched. Therefore,
>         PPI does allow
>         > inferences about directed coupling, but it cannot
>         disambiguate between the
>         > two directions on its own. The disambiguation must come from
>         other
>         > evidence
>         > you might have about how the two regions are connected to or
>         influencing
>         > each other. I had a discussion with Karl Friston several
>         months back about
>         > this, and had promised to post it to the list at some point
>         so here it is.
>         > Note that when Karl refers to increase and decrease below he
>         is
>         > distinguishing between the reciprocals of the slopes of the
>         regression
>         > plots. So the slope or beta of A vs. B is the reciprocal of
>         the slope
>         > (beta)
>         > of B vs. A. He doesn't mean increase or decrease in the
>         absolute sense.
>         >
>         > "A PPI does not disambiguate between an anti-symmetric
>         interpretation of a
>         >> directed PPI effect. In the sense that P could increase the
>         influence of
>         >> A
>         >> on B or it could decrease the influence of B on A. Both are
>         potential
>         >> interpretations of a significant PPI. However, the
>         influence is
>         >> certainly
>         >> directed. This issue has been discussed before and is
>         easily resolved by
>         >> making it clear that one is testing a specific null
>         hypothesis (ie.e.,
>         >> that
>         >> P increased the coupling between A and B), noting that this
>         precludes
>         >> post
>         >> hoc interpretations of a significant result (e.g, P
>         decreased the
>         >> reverse
>         >> coupling).  In short, PPI does allow for inferences about
>         directed
>         >> coupling
>         >> but it cannot be used to disambiguate between alternative
>         anti-symmetric
>         >> hypotheses."
>         >>
>         >
>         > For a  good example of inferring directionality opposite to
>         how we usually
>         > interpret PPI's see the article by Grabenhorst & Rolls, J
>         Neurophysiol,
>         > 104:1649-1660, 2010. In this case a source region was in the
>         orbitofrontal
>         > cortex and the target that came up in the PPI was in the
>         prefrontal
>         > cortex.
>         > However, the directionality was inferred to be from the
>         prefrontal to the
>         > orbitofrontal cortex based on the top-down relationship
>         between the areas
>         > and that attentional modulation is more likely to come from
>         the prefrontal
>         > cortex.
>         >
>         >
>         >>
>         >> >> 2) What exactly does "contribution" mean?
>         >> >> It is the influence one area ("seed") exerts over the
>         other
>         >> ("target"),
>         >> >> and the influence depends on the psychological factor.
>         Could this
>         >> be
>         >> >> interpreted as that the information flow of the seed to
>         the target
>         >> is
>         >> >> increased, depending on psychological state? Or is this
>         >> >> over-interpreted?
>         >> >
>         >> > Its not just flow, but the magnitude of the flow that
>         changes.
>         >> > Remember, these are beta estimates not simply correlation
>         >> coefficients
>         >> > that are being compared.
>         >> Yes, that's what I meant. Isn't your statement here (no
>         correlational
>         >> approach) in disagreement what you have written for
>         question (1) above
>         >> (it is corr. approach)?
>         >>
>         >
>         > I don't think the statements are in conflict. PPI is not a
>         correlation,
>         > but
>         > in a sense it is a correlational-type of approach. What
>         distinguishes it
>         > is
>         > that main effects are explicitly discounted and again you
>         have chosen the
>         > direction of the influence.
>         >
>         >
>         >>
>         >>
>         >> >> 3) Karl Friston made a comment on the list which I can't
>         follow:
>         >> >> https://www.jiscmail.ac.uk/cgi-bin/wa.exe?
>         A2=SPM;41a9f073.0903
>         >> >> [..]This is because an increase in the regression
>         >> >> slope of area A on area B can be interpreted as an
>         increase in the
>         >> >> effective connectivity (under an instantaneous and
>         >> >> linear model of effective connectivity) from B to A.
>         However, one
>         >> can
>         >> >> transpose the regression (i.e., switch the axes)
>         >> >> and interpret it as a decrease in effective connectivity
>         from A to
>         >> B."
>         >> >
>         >> > Specific to the interaction term.
>         >> Although I wasn't able to follow your example, it seems
>         indeed to be
>         >> specific for the interaction term. I again made up some
>         data, but this
>         >> time including an interaction. When the predictors are
>         changed the
>         >> interaction regressor has to be recalculated as well and
>         consequently,
>         >> the interaction changes as well. However, although the sign
>         changes
>         >> indeed as well, the beta-value does also change and,
>         consequently, the
>         >> significance of the interaction term changes. So, it seems
>         to me that
>         >> although Karl's comment is true in terms of the basic
>         pattern one might
>         >> observe (increase/decrease in connectivity), it is
>         potentially
>         >> asymmetric in the way that the interaction is significant
>         in the one way
>         >> (regression A on B) but not in the other way (regressing B
>         on A) - or
>         >> vice versa.
>         >>
>         >> Thus, if I understood Karl's comment correctly and I'm
>         wrong with my
>         >> arguments (the latter the most likely option) I could
>         conclude the
>         >> following: When I find, for instance, that under attention
>         (as opposed
>         >> to no attention) the contribution of region A to region B
>         increases in
>         >> terms of PPI, I could make the following conclusion:
>         >> "Attention increases the information flow from region A to
>         region B.
>         >> Alternatively, attention decreases the information flow
>         from region B to
>         >> region A."
>         >>
>         >> When I am right with my arguments, I could conclude only
>         "Attention
>         >> increases the information flow from region A to region
>         B." (there is
>         >> still the alternative interpretation of activity in region
>         A affects the
>         >> amount to which attention modulates activity in region B,
>         see Friston et
>         >> al. 1997).
>         >>
>         >
>         > Yes there is the alternative explanation, but Karl had this
>         to say about a
>         > similar question I posed:
>         >
>         > "PPI is never concerned with disambiguating between two
>         alternative
>         > hypothesis (i.e., A to B or B to A). It is used to reject
>         the null. In
>         > this
>         > sense,directionality can be inferred because one specifies
>         the alternative
>         > model in terms of a particular direction. All one has to
>         remember is to be
>         > very clear that one PPI hypothesis is being tested. Note
>         that there are
>         > many
>         > alternative models that can explain many classical
>         inferences but we do
>         > not
>         > usually worry about that."
>         >
>         > I hope this helps,
>         >
>         > Darren
>         >
>         >
>         > --
>         > Darren Gitelman, MD
>         > Northwestern University
>         > 710 N. Lake Shore Dr., 1122
>         > Chicago, IL 60611
>         > Ph: (312) 908-8614
>         > Fax: (312) 908-5073
>         >
>         >
>         >>
>         >> Best regards,
>         >> Andre
>         >> --
>         >>
>         >> ______________________________
>         >>
>         >> Dr. Andre J. Szameitat
>         >> Department Psychologie
>         >> Neuro-Cognitive Psychology
>         >> Ludwig-Maximilians Universität
>         >> Leopoldstrasse 13
>         >> 80802 München, Germany
>         >> Tel. +49-(0)89-2180 6778
>         >> Fax. +49-(0)89-2180 4866
>         >> www.psy.uni-muenchen.de/ncp
>         >>
>         >> Office: Martiusstr. 4, Room 6
>         >> ______________________________
>         >>
>         >
>
>
>
>
>
> --
> Darren Gitelman, MD
> Northwestern University
> 710 N. Lake Shore Dr., 1122
> Chicago, IL 60611
> Ph: (312) 908-8614
> Fax: (312) 908-5073




--
Darren Gitelman, MD
Northwestern University
710 N. Lake Shore Dr., 1122
Chicago, IL 60611
Ph: (312) 908-8614
Fax: (312) 908-5073