in this message over and talk about how analysis of mediation and moderation in

particular have two very simple and powerful techniques for a presence in

the social sciences now in her own aging as well so there are two basic kinds of

collectively that we have been and will be talking about the first kind is what

we call the data reduction approach and did a reduction approaches identify

distributed patterns in the data they explained very complicated 3d 4d five

dimensional datasets as a simple combination of in our case temporal

company ads and spatial components and then subject of our compounds and these

include standard and try to interview techniques like principal components

analysis and independent component analysis partial least-squares is a

variant that takes into account multiple predictors and it is side and multiple

outcomes multi-way algorithms extend beyond two dimensions these include

things like cancer ICA and peres FAQ and factor analysis and in Scotland haskell

individual differences multidimensional scaling and finally other techniques in

the computational editor like self-organizing maps and often graph

theoretic approaches are applied to these mats in order to you characterize

the whole network properties and that’s increasingly popular now the second

family is the path modeling family and the utility of this is to provide

inferences about specific connections and associations in the brain and with

physiology and behavior and experimental variables include the following things

path models are set series of linear models unobserved variables and

structural equation models are very somewhere they work on a work on

associations across variables

a psychophysiological interaction analysis is a particular kind of iPad

model is also spectral coherence models in the in the frequency domain instead

of the time domain and there’s also Granger causality

models which can take into account crossed like croatians and other

coalition and dynamic causal models which is part of a family of state-space

models that estimate relationships based on the dynamics or derivative so the

responses these different approaches can be complimentary so for example you can

use a deduction strategy like ICA come up with components and then you can do

path models or other kinds of models on this company’s course so this is really

I think of this as a as a tool box for things that you can do to help

understand your data and make interesting inferences so we’ll talk

about mediation in particular here in mediation is is really an important

concept and we can think of it in part as a search for mechanism so let’s say

I’ve got a manipulation of expected pain relief and observing some analgesia pain

relief and we can think of mediating variables as those that might intervene

explained that effect so this could be caused by a less attention to the

symptoms alternate valuation of pain inducing events and it could be caused

by decision by other kinds of processes like that when we apply this to a brain

and now says

really advantage is that it can’t connect experiment design variables

frame measures and how comes in a single integrated model where otherwise there’d

be a series of models to have gotten experiments manipulation measures in

this series of brain regions which are potential mediators of that fact and and

how come

behavior that’s like now looking more detail mediation to mediation the idea

of what is testing is does this period

explain some of the relationship between X&Y this is really all about these texts

the initial rowly is the outcome these initial variable outcome relationships

and it helped establish a pathway that connects X to Y through some intervening

variable so for example the brain I might apply a stressor thats experiment

of rebel attacks and is in its activity enters cortex and why is increases in

heart made

we also commonly referred to these paths the relationships by letters so by

convention well both say that the x10 relationship has passed a the m2 I

relationship controlling for access path be the original relationship

text y Paz sea and the relationship between X&Y controlling for me

moderation is this test something that’s different what is testing is does the

level of my moderator now influence the relationship between X&Y so this can

establish regulation of a pathway or conditionality of a pathway and one

common way to diagram is like this and in this case for example I stressors a

moderator and now we’ve got the relationship between enters in that

activity in heart rate being different when stresses on Britain’s off now

stresses a moderator so let’s look into how test the mediation again and one way

to think about this is the model comparison so ab&c are all in all slopes

in standard regression equations so in the first equation we take grass and my

acts and in the second equation we regress why the outcome line and acts

together so here’s why

era and in that kind of attention this is what it looks like I’ve got a vector

of observations and mediator I’ve got a dinner set and a predictor acts and

those are each multiplied by which the intercept time times the the intercept +

path a time Zacks the second equation looks like this so now I’ve got

intercept a the acts and the AM variables in my design matrix and I’m

estimating see prime in be controlling for the other

so weird thing about this model comparison in terms of carrot actuals so

what we’re doing is we’re comparing the situation the right with us just X&Y

giving up a scene with the situation and all that we’re now I have some of that

relationship going through and through this medium pathway into the character

actually is if we could put a clamp on and prevent it from burying with the

effect of X&Y be reduced or absent and if so there’s mediation if that’s the

case then if we compare patsy and passive prime they should be different

and so we can test the significance of C minus see prime and that’s the test of

mediation and this with some algebra is actually turns out to be the same as

testing the product of the path coefficients A&B so we’re really testing

and baby product in this case so this is a directional model where I have to

specify which is the picture in which is the outcome but 102 caution it’s better

not to make strong directional interpretations about which is causing

what I’m not sure experimental manipulating variables and there has

been a lot of debate and controversy about mediation and as far as I can see

a lot of this controversy centers on whether you should make strong causal

inferences when you have observed variables and I don’t believe you can I

don’t think that means the models are not useful I think that it just means

that we have to be careful about the inferences that we make I’m so one thing

to note here is that we can reverse the direction of the arrows and often get

somewhere effects we could reverse the which is the AM which is the wife and we

might get similar effects as well and one contestas different models but it’s

important to know that the best direction with which model seems to give

them a significant results depends not only on the underlying strength of

relationships but also on the relative error variances so one variants can be

greater than another 14 uninteresting reasons for example if it’s a brain

region could just be a noise your estimate and then it’s going to look

less like a mediator and finally causal inferences generally safer at least only

affects

Mr experimentally manipulated so we can still uses multiple pathways but perhaps

without making strong causal planes so mediation test is a statistical test of

a times be and what that means is that we need to have an estimate a time to be

divided by

estimator of its dinner there so this is the soho tester the Iranian version of

several versions and this is the says that the ATMs be divided by as many as

general there are distributed normally as these core and then you can get

people use to make inferences well a times be it’s not actually normally

distributed most often and so this test turned out to be over conservative and

it’s now typically replaced with the bootstrap tests and many people have

worked on bootstrapping in mediation now and there’s packages available for that

multiple multiple software packages and now at the bottom of you think about

these paths and happy effects it’s useful to think about the the families

this is a vendor and the families of all the possible significant test so what

you see here in the one circle Marte is all the family of all the tests that

have a significant pate effect and the green circle as all the tests have a

significant effect and a certain subset of them will overlap to get a and B the

conjunction and then a subset of those are going to be ones in which the ATMs

be path coefficient insignificant so you can see from this that the mediation

process is really a relatively conservative test for the presence of a

patent app at the effect but also whether they’re covariances are are

strong or or whether the joint effects are strong enough to pass the mediation

test let’s look at a graphic example of this is that we are working with our

case where we have a stressor influencing anterior cingulate activity

in the brain which is predicting heart rate increases to the stressor and this

is what it looks like graphically will first look at a case with us mediation

on the top panel so now the blue dots or stress on the Green Dot stress off and

the pathway effect is rather low as having green on

X axis which is anterior cingulate so we can see here indeed the blue dots are

shifted to the right so there is a path in fact that path be effect is the

effect anterior cingulate activity on heart rate controlling for this dresser

so this end up being a parallel slopes liner and cover model and we can see

that happy there is the slope of that line on average across the two groups so

that’s positive

the more interesting is that the greater the heart rate controlling 44 group

cassie is just this simple effect of stress on her train so that’s where the

blue dots are higher than agreeing on the y axis and indeed you see effect

here and pasty Prime is the difference after you control centers England for

the for the mediator and so that’s this gap between the two parallel lines and

as you can see here the gap is very small so we have a policy effect is

going down to virtually zero and that means that humanity Prime is is greater

than 0 and there’s a mediation effect so into it we have a mediation effect what

are we doing well what we’re saying is that the amount the effect of the stress

on the heart rate is exactly what I predict based on the interesting

activity so just shifting up along the interesting you access and that gives me

the significant mediation effect on the bottom panel let’s look at the case with

their significant paths in the effects but there’s no mediation and in this

case to be similar situation except that the effect on the stress on the heart

rate is so large and the path a nap at the effects are relatively small so

they’re really not sufficiently large to explain the effect so I’m left with is a

big C and a pretty big C prime went to control 444 interesting activity so that

gap is still there and that means that the mediator can’t really explain a lot

of that

relationship