Good, it sounds like we are in agreement then that one must be careful
regarding making directional statements based on PPI. I think it was
important to make that clear to avoid confusion.
Thanks for the discussion as well.
cheers,
-MH
On Sat, 2011-01-22 at 21:32 -0500, Darren Gitelman wrote:
> 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
>
|
