On Sat, 11 Nov 2000, Ick-Joong Chung wrote:
> I have a question about two-sample problem. I am comparing coefficients
> of two samples (poor and non-poor) and would like to investigate whether
> the difference between two coefficients is statistically significant ('one
> on one' level as well as 'overall' level). To compare coefficients from
> the two datasets in OLS settings, I can just use a two-sample t-statistic
> with a pooled variance estimate obtained from the models. I am wondering
> whether this can be applied to multinomial logistic regressions.
> Alternatively, someone might suggest interaction terms.
This would seem the most straightforward approach.
> But unfortunately, it doesn't work for me because there are less power
> and sparsity issues involved when I create as many interaction terms as
> predictors.
I do not understand this remark. You have a model with p predictors,
applied in sample 1, which must have sufficient d.f. for the analysis
or you would not have a coefficient to compare: that is, n1 is enough
larger than p+2 that you have a respectable number of d.f. for error,
dfe1; similarly for sample 2. When the samples are combined to test for
equality of coefficients between samples, you have 2p+1 predictors:
the original p , plus a dichotomous indicator (which sample), plus p
interaction terms (products of the original p predictors with the
indicator). You also have n1 + n2 observations, with dfe1 + dfe2 - 1
degrees of freedom for error. Where is the loss of power, and what are
the "sparsity issues", that I evidently do not perceive?
-- DFB.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
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