Re: Comparing coefficients

Many thanks for the reply.

The example I provided stylizes my particular situation. My data
actually comprises of dyads of firms. There is a wide difference in the
p values: .007 vs. .281. Husband's education does not have a
significant impact on wife's income. But the effect size does seem
somewhat higher: .004 vs. .002. I also restated the data as own
education and spouse's education and created one large dataset with
double the observations. In general, would there be any issues related
to inference in this data set? Suppose for example my hypothesis was
that own education will have a positive impact, while spouse's
education will have a negative impact. Can I take this larger data set
with twice the number of observations and do conventional tests for
significance of coefficients? Or does the fact that each observation
comes from a dyad cause any biases?

Thanks in advance for the help.

Shyam

Richard Ulrich wrote:
> 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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