Michael:
Perhaps it is a terminology thing, but what do you mean by "PPI allows
an inference about directionality because you have specified thealternative 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