st: Re: coefficient explanation

[Joseph Coveney <stajc2@gmail.com>]

Kayla Bridge wrote:

The model I am working with now is:
y=beta1*x1+beta2*x2+u   (here, beta1 is significant)
However, I realize the correlation between y and x1 is due to some other factor
which is not present in the model. Therefore, I add this critical variable that
can best proxy for this factor, x3, in the model. Now the model is
y=beta1*x1+beta2*x2+beta3*x3+u. In this case, beta1 should weaken when x3 is
present. But my question is: beta1 should have smaller magnitude than before but
still significant or beta1 should be insignificant when x3 is added? If beta1 is
still significant but with smaller value when x3 is added, can I say x3 is a
critical value which is ignored before or correlation between y and x1 is
weakened?

Any suggestion is appreciated.

--------------------------------------------------------------------------------

It sounds like you're analyzing data from an observational study.  Maarten Buis
has posted on this list before on what can happen to the magnitudes and signs of
regression coefficients when additional variables are added to a regression
model of an observational study.  You might want to search the archives for some
of his posts.

You seem to suggest that your subject matter knowledge tells you that the
apparent association between y and x1 is illusory, that in reality it only
reflects the action of some other factor on both.  If so, then is there a good
reason to include x1 in the model at all, especially if you have in hand a
halfway-decent measure of this other factor, namely, x3?  If your subject matter
knowledge allows, you might consider modeling the relationships between y, x1
and x3 (and x2) by means of path analysis or even a structural equation model if
your dataset has enough indicator variables to assure model identification.
(Type "help sem" in Stata's command window for more information.)

I assume that your model actually does have an intercept, that its omission in
your post is inadvertent.

Joseph Coveney


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