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Topic: Interpretation of coefficients in multiple regressions which model
linear dependence on an IV

Replies: 146   Last Post: Dec 15, 2012 6:44 PM

 Messages: [ Previous | Next ]
 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: OK – I think I’m set, at least till we get t
o c on (e, u, u*e).

Posted: Nov 28, 2012 5:59 PM

On Nov 27, 6:19 am, djh <halitsk...@att.net> wrote:
> [...]
>
> 4.
>
> Apart from correcting the general theoretical deficiency which you
> perceive as arising from uL/uH dichotomization itself, another benefit
> of doing the re-analysis with the three new regressions is presumably
> that it will help us improve the two tables I presented at the end of
>
> Table I:
>
> Extent to which Significant 3-way Interactions
> across Length Intervals
> are Exhibited at Specific Length Intervals
> (Data Not Shown for 2RS and 2RC)
>
> 3-way u Non-Random
> Coeff Len Int p Lev 2S 2C % Chg
> eS ALL .014 L 2.288 6.075 165.5%
> H 7.993 8.309 4.0%
>
> 1 .035 L 1.578 6.545 314.6%
> H 5.719 4.760 -16.8%
>
> euSe ALL .005 L 2.402 6.154 156.2%
> H 8.265 7.975 -3.5%
>
> 1 .025 L 2.076 6.640 219.8%
> H 6.002 3.926 -34.6%
>
> 4 .011 L 1.250 7.881 530.3%
> H 10.755 7.658 -28.8%
>
> uS ALL .0003 L 0.277 -0.082 -129.6%
> H 0.050 -0.848 -1796.0%
>
> 5 .040 L -0.287 -0.345 20.0%
> H 0.289 -0.325 -212.3%
>
> 9 .0002 L 0.548 -0.078 -114.2%
> H 0.436 -1.056 -342.4%
>
> 10 .011 L 0.563 -0.006 -101.0%
> H 0.261 -1.103 -522.9%
>
> 11 .032 L 0.617 -0.142 -123.1%
> H 0.354 -1.178 -432.9%
>
> euSu ALL .036 L 0.240 -0.037 -115.4%
> H -0.190 -0.760 300.0%
>
> 9 .008 L 0.482 -0.067 -113.8%
> H 0.141 -0.829 -686.3%
>
> 11 .012 L 0.415 -0.083 -120.1%
> H 0.185 -1.253 -777.3%
>
> Table II:
>
> Bonferroni Correction of p?s in Table I
>
> TstVal=
> .025/ p(j)-
> j Category p(j) (14-j) TstVal
>
> 1 uS-9 .0002 .00192 -.00177
> 2 uS-ALL .0003 .00208 -.00178
> 3 euSe-ALL .005 .00227 .00264
> 4 euSu-9 .008 .00250 .00559
> 5 uS-10 .011 .00278 .00779
> 6 euSe-4 .011 .00313 .00784
> 7 euSu-11 .012 .00357 .00819
> 8 eS-ALL .014 .00417 .01032
> 9 euSe-1 .025 .00500 .02016
> 10 uS-11 .032 .00625 .02528
> 11 eS-1 .035 .00833 .02701
> 12 euSu-ALL .036 .01250 .02366
> 13 uS-5 .040 .02500 .01523
>
> In particular:
>
> (A) with respect to the equivalent of Table I that will be constructed
> from the new 2-ways, I am hoping first that more of the new 2-ways at
> specific length-intervals will show probabilities < .05, as opposed to
> the paltry yield of ?good? interval-specific 3-ways in the current
> table.
>
> (B) with respect to the equivalent of Table II that will be
> constructed from the p?s in the new Table I, I am hoping that more of
> these p?s (both cross-interval and interval-specific) will withstand
> plausible Bonferroni correction.
>
> Is there any reason to assume A PRIORI that (A-B) will not be the
> case, due to some subtle theoretical reason that I?m too ignorant to
> see? And more generally, is there a better pair of tables that should
> be generated for the new 2-ways, instead of tables like (I-II):
>
> Also, just out of curiousity, I?m wondering if it would be legitimate
> to ?allow? row 3 in Table II as well as rows 1 and 2? (You mentioned
> once that some manual tinkering with Bonferroni results is allowable.)
>
> Thanks as always for your considered consideration of these matters.
> It will take me 2-3 days to add code and re-run for c on (u,u^2) with
> computation of a first-cut ?average? slope, depending on day-job
> demands.
>
> In the meantime, I?m hoping you?ll continue your exegesis with an
> explication of c on (e, u, u*e), the second of the three new
> regressions.

re Table I: "% Chg" (percent change?) is not a good measure here.
The analysis itself looks at the simple differences. Percent change,
(or its alternate form, relative difference) is rarely appropriate
when the two values involved can have different signs.

re Table II: The trick is to compare p(j)*(14-j) to alpha, instead
of comparing p(j) to alpha/(14-j). That way you can simply scan down
and see what you would have to change your chosen alpha to in order
to declare the j'th test "significant". Thus, .005 * (14-3) = .055,
which is twice your chosen alpha (.025) and so should probably not be
called significant.

Also: why .025 instead of .05? Are the p's one-tailed when you really
want them to be two-tailed? Such things should be part of the report.

Date Subject Author
11/21/12 Halitsky
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