David M. Goldstein (2001.08.21.1241pm)

Bill Powers and Jeff Vancouver responded to my message. Actually, Jeff seems

to already be using a more sophisticated version of the method in the

article. However, I will give an explanation a try, by means of an example.

Jeff can probably tell us more.

Suppose that we want to find out if "attention/concentration" makes a

difference in how well a person controls in a pursuit tracking task. The

treatment effect is the ease/hardness of the task. Is

attention/concentration a mediator or a moderator?

As a mediator, attention/concentration causes the treatment effect, by

definition. As a moderator, attention/concentration affects the magnitude of

the effect.

Suppose that a person is doing a pursuit tracking task. Let us say that a

person does the task 10 times for 2 minutes each time. We pick a disturbance

function randomly for each trial. This varies the ease/hardness of the task.

We divide the distribution of disturbance functions in half, one-half above

and one-half below the median. This defines two treatment conditions: easy,

below the median and hard, above the median.

This experiment is repeated for 25 subjects.

The outcome measure is the stability statistic for each trial. For each

person we look at the difference score for the Hard-Easy task.

The person is hooked up to an EEG machine that measures his EEG at the FZ

10/20 location. For each trial, we record the theta/beta ratio. This ratio

is often thought of as a measure of concentration/attention. The theta/beta

ratio is the variable we want to test if it is a mediator or moderator.

So, for 25 subjects we have three variables: (1) Outcome Difference score

for the Hard-Easy Task, (2) Theta/beta ratio for Hard - Theta/beta ratio for

Easy, (3) Theta/beta ratio for Hard + Theta/beta ratio for Easy.

We do multiple regression statistical analysis of variable (1) against

variables (2) and variables (3).

" To asess both mediation and moderation due to a concomitant variable that

varies between treatment conditions, one regresses the Y difference on both

the X sum and the X difference. Assuming that there is an overall treatment

effect on X and that the X difference predicts the Y difference, mediation

of the treatment effect in Y by X is indicated (assuming that X and Y are

scaled to have a positive relationship and the treatment effects in Y and X

are in the same direction). If the X sum is predictive of the Y difference,

then X also serves as a moderator of the treatment effect and, equivalently,

X relates to Y differently in the two treatment conditions. Finally, if the

X sum has been centered, then the intercept in this regression equation will

equal the the magnitude of the residual treatment difference in Y, over and

above mediation due to X and the mean of value of X. In other words, it will

equal the portion of the mean treatment effectg that is not mediated through

X."

This is probably as good as I understand it right now.

Attention/concentration could be a moderator and/or a mediator factor or

neither.

In the pursuit tracking task, if a person stops trying to control,

attention/concentration is focused off the task. In the sense that

concentration/attention must be present for any degree of control to be

present, it should turn out to be mediator. If a person is simultaneously

attending/concentrating on other stuff, performance will not be as good.

Attention/concentration should therefore turn out to be a moderator as well.