On Tue, 3 Jun 2003, Carlos J. Vilalta y Perdomo wrote:
> Would you please give me some advice in the following problem?
> Problem:
> Pearson correlation of x1 with y is n.s.
By this you must mean that the zero-order correlation is not large
enough to be interesting (i.e., "significant"). This of course says
nothing whatever about 1st-, 2nd-, ..., order partial correlations
between x1 and y, "partialling out" one or more other variables.
> Yet, when y = x1 + x2 + x3... + x6 + e, then x1 becomes a
> significant predictor of y
Which is to say, the 5th-order partial correlation between x1 and y,
partialling out x2, x3, x4, x5, and x6 (aka r_y1.23456), is large enough
to be interesting and useful.
> Questions:
> 1. Would this be effect of an intervening/mediating variable?
"This" is a tad ambiguous. If you mean "the difference in magnitude
between the zero-order correlation and the 5th-order correlation", it
would be the effect of the interrelationships of one or more of the
variables {x2, x3, x4, x5, x6} with y, with x1, and/or with each other.
Whether it be reasonable to call any (or all) of these five variables
"intervening" or "mediating" depends in part on how you perceive the
7-dimensional relationship among them all, in part on which (if any) of
these variables are under your control, and in part on what you want to
mean by the adjective(s) (that is, by "mediating" and "intervening").
> 2. What would you do? Include or exclude x1 from the analysis?
Insufficient data. Do you intend to exclude any of {x2,...,x6} from the
analysis? If so, (1) why and (2) how does x1 behave in the reduced
model thus obtained (that is, obtained by excluding one or more of
{x2,...,x6})? What do you mean when you write "x1 becomes a significant
predictor of y"? Do you mean that the t-test (or the equivalent F-test,
whichever your software reports) for the partial regression coefficient
b_y1.23456 has p < alpha? (That's what _I_ would have meant. But you
may mean only that the global F-test with 6 d.f. has p < alpha, which
does not really say anything about x1 in particular.)
What is the purpose of the regression analysis? Finally, if x1 is
significant in the model you are contemplating, why would you wish to
exclude it?
> I appreciate your comments and suggestions.
> Carlos
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