Re: Linear Regression to study the mediating effect of a var

On May 30, 1:35 pm, quebecs...@xxxxxxx wrote:
Hi everyone,

I have received a new statistics piece of work: I am asked to study
the mediating role of a variable X on a variable Y. The analysis that
is suggested to me is the "Hierarchical Linear Regression Analysis". I
do not know that topic and that particularl analysis because I am
trained as a mathematical statistician. I would be grateful if
somebody could indicate to me how to run that Linear Regression in
order to study the mediating effect of X.

I greatly appreciate your help and/or pointers.


This link is useful:
http://www.unc.edu/courses/2006spring/psyc/050/001/partials.html

The relevant paragraph is

Partial Correlation:

For the sake of generality, let X and Y be the two variables we have
found to be correlated. I'll use r(X,Y) to represent their
correlation. We'll call r(X,Y) the simple correlation.

We introduce a third variable, Z, which may or may not mediate the
relationship between X and Y. We can find out if Z is a mediating
variable by calculating the partial correlation of X and Y,
controlling for Z. I'll write the partial correlation as r(X,Y|Z). The
mediating variable is the one to the right of the vertical line.

In other words, r(X,Y|Z) is a measure of the relationship between X
and Y if we control for Z: if statistically we hold Z constant. If
r(X,Y|Z) is much smaller than r(X,Y), we can conclude that Z is a
mediating variable. It may explain, at least in part, the observed
relationship between X and Y. Be careful, though. Although we talk
about "explaining" the relationship, based on correlations alone we
will never know what "causes" the relationship.

In the big toe example, X is a measure of language skills, Y is size
of the big toe, and Z is a child's age.

If you have three variables, there are three simple correlations among
them, r(X,Y), r(X,Z), and r(Y,Z). Knowing these three correlations,
it's very easy to calculate the partial correlation r(X,Y|Z). You can
use this calculator for the purpose.

Suppose r(X,Y) = 0.40, r(X,Z) = 0.55, and r(Y,Z) = 0.65. Then r(X,Y|Z)
= 0.07 (be sure you can duplicate that result). That is, the
correlation between X and Y is close to zero when Z is introduced as a
mediator. Age explains the relationship between language and big toe
size.

Hope this helps

.

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