Re: Comparing coefficients

On 22 Nov 2005 16:47:05 -0800, "Shyam" <mvshyamkumar@xxxxxxxxx> wrote:

> Hi:
>
> I have a sample comprising of dyads (e.g. husband-wife). For each dyad
> I have two dependent variables (e.g. husband's income, wife's income),
> and a set of independent variables (husband's education, wife's
> education). I conducted two separate regressions:
>
> Husband's Income = a1 Husband's Education + a2 Wife's Education
>
> Wife's Income= b1 Husband's Education + b2 Wife's Education
>
> My hypothesis is that a2> b1. On conducting the two regressions I find
> that a2 is significantly greater than 0, while b1 is not. Is that
> sufficient to confirm my hypothesis? Are there any formal tests that I
> need to conduct? The chow test comes to mind, but I'm not convinced it
> applies.

Your apparent conclusion seems reasonable to me, but the
rules of statistical logic don't let you say the hypothesis
is confirmed. You might point to the "effect sizes" as an
additional argument. Do the regression coefficients differ
greately? Do the *p-values* differ greatly? I'd say, one
test of 0.06 versus a test of 0.04 is not convincing at all

You could apply the Chow test if you re-state the variables
as "own education" and "spouse's education." Then the
purely statistical problem would be that the actual data
probably exists as pairs (husband and wife).

Another problem for inference is the confounding between
their educations, and the further confounding caused by
who-might-help-whom get a better job. Then, there is the
potential difficulty of putting "education" on a simple scale.
Unless that's only supposed to be "Years of high school
and college".

Since this is observational data, you have a heavy burden
of trying to argue that there are *no* artifacts that might give
you the result you observe -- artifacts arising in logic or
because of measurement problems. You probably can't
answer them all, so you do the best to can to build as good
a case as you can, including arguments from anecdotes.



--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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