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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 ]
 Halitsky Posts: 600 Registered: 2/3/09
Posted: Dec 7, 2012 9:07 PM

I. You wrote:

1. What does "(Fold,Set,Len) = (all,all,all)" mean?

Just my stupid way of saying that the reported Subset x MoSS values
were obtained by averaging across all six folds, all six sets, and all
lengths meeting the ?four-way content? criterion (data for S,N, data
for C,N, data for S,R, and data for C,R). I think you said that
anything NOT mentioned is assumed to be averaged over, so perhaps I
should have left out the ?|? (at) clause entirely.

II. You wrote:

2. Something's wrong somewhere. Those p's are too similar to one
another, and are too large to be consistent with the other results
you've been reporting.

No ? it?s just that the ?good? and ?great? p?s for u^2 are very length-
specific, as is shown by the following table for u^2 in regression c
on (e,u,u*e,u^2) for Len | subset = S, method = N, fold = a1, set = 1.
(Note that this table is sorted by increasing p.)

So the question posed by the following table is the same basic
question I actually asked several posts ago, namely: for (S, N, a1,
1), do we have ENOUGH ?good? and ?great? p?s to claim that the model c
on (e,u,u*e,u^2) ?works? in a sufficient number of cases to ?keep? it,
at least for the factor combination S, N, a1, 1) ?

Also, please note that similar tables exist for all of the factor
combinations equivalent to (S, N, a1, 1), so is it possible we should
actually be comparing the distributions of p for u^2 from all these
different factor combinations ... to see which distributions of p are
?left? of others and ?right? of others in the horizontal sense (i.e.
with p as the x-axis)?

u^2 (t, df, p) Table: t, df, and p values for u^2 in regression c on
(e,u,u*e,u^2) for Len | subset=S, method= N, fold=a1, set=1

Len t df p

71 3.930 24 0.00063
26 3.434 44 0.00131
122 3.565 16 0.00258
24 3.162 47 0.00274
27 3.101 58 0.00297
110 3.396 16 0.00369
101 3.179 19 0.00494
35 2.870 59 0.00569
84 2.460 27 0.02058
109 2.462 25 0.02108
25 2.343 66 0.02216
73 2.185 31 0.03654
69 1.989 34 0.05474
62 1.988 24 0.05828
49 1.922 39 0.06193
55 1.929 31 0.06294
44 1.733 35 0.09186
37 1.667 68 0.10004
28 1.635 64 0.10697
54 1.639 33 0.11063
94 1.638 22 0.11567
41 1.616 32 0.11598
29 1.564 74 0.12219
30 1.546 64 0.12705
60 1.533 34 0.13462
75 1.510 20 0.14672
33 1.464 54 0.14893
66 1.451 35 0.15580
52 1.404 38 0.16830
74 1.394 25 0.17562
50 1.240 40 0.22236
32 1.216 47 0.22989
67 1.186 40 0.24280
63 1.147 28 0.26105
38 1.084 38 0.28513
53 1.065 33 0.29463
40 1.053 46 0.29789
68 1.064 19 0.30072
77 0.998 28 0.32687
58 0.989 32 0.32996
76 0.950 22 0.35222
48 0.873 38 0.38816
43 0.860 33 0.39616
80 0.807 31 0.42564
46 0.766 30 0.44947
87 0.717 17 0.48337
56 0.679 31 0.50249
45 0.677 29 0.50349
83 0.659 19 0.51765
96 0.644 23 0.52619
59 0.537 24 0.59645
61 0.490 39 0.62669
36 0.454 57 0.65159
39 0.443 30 0.66063
65 0.424 21 0.67621
120 0.390 16 0.70203
95 0.325 12 0.75075
51 0.288 45 0.77443
108 0.270 14 0.79079
31 0.234 65 0.81572
90 0.169 14 0.86841
111 0.124 18 0.90264
34 0.078 73 0.93820
47 0.065 45 0.94811
89 0.061 11 0.95249
42 0.002 31 0.99881

III. You wrote:

?In particular, you should not be considering any results from
regressing c on (u,u^2) if e matters?.

I'm sorry to plead ignorance but nothing you've ever posted before has
prepared me to understand you here at all. What I mean by this is the
following.

From the beginning we have been using a regression involving e, a
regression involving u, and a regression involving (e,u) IN CONCERT,
NOT as mutually exclusive alternatives.

1a) ln(c/L) on ln(c/e)
1b) ln(c/L) on ln(c/u)
1c) ln(c/L) on (ln(c/e), ln(c/u))

simplified to

2a)c on e
2b)c on u
2c)c on (e,u)

and that actually improved matters.

And then finally, because of your very remarkable intuition that the
?L/H? dichotomization of u should be replaced by adding u-related
factors to the regressions themselves, we have arrived at

3a) c on (e,u,u*e), by addition of a u-factor to c on e
3b) c on (u,u^2), by addition of a u-factor to c on u
3c) c on (e,u,u*e,u^2), by addition of two u factors to c on (e,u)

So ... if we never intended 1(a-c) as mutually exclusive alternatives,
nor 2a-c as mutually exclusive alternatives, why all of a sudden do we
have to treat (3a-3c) as mutually exclusive alternatives? Please
recall here that the ultimate goal was always to develop predictors
for logistic regressions, and back when we were doing logistic
regressions, you said it?s best to throw everything into the soup that
one can think of ... that?s why we had logistic regression predictors
based on MORE THAN ONE linear regression.

Also, why is NOT statistically legitimate to postulate that there are
BOTH:

a) a relationship between c and u that, as you suspected, is best
expressed by c on (u,u^2) because the relationship changes with
increasing u

b) a relationship between c and e that, again as you expected, is best
expressed by c on (e,u,u*e) because again, the relationship changes
with increasing u.

IV. You wrote:

?4. SEP = sqrt[Residual Sum of Squares / df]
= sqrt[Residual Mean Square]
Are you sure Ivo's program doesn't give that as optional output??

He provides:

rsq(), where rsq = ?sse? / ?sst?
sigmasq(),
ybar(),
sst(),
k(),
n()

and I have a feeling that rsq is what you?re looking for. But if you
can?t say for sure, then what I?ll do is a complete rerun that
generates all of them and then compare each to the Excel Standard
Error of Prediction for the entire regression (not for any particular
coefficient.)

V. You wrote:

?5. Let the constant in the input to Ivo's program default to 1.?

OK.

VI You wrote:

?6. I have a hunch that Het may be related to a Subset x Fold
interaction, where the d.v. is the average slope.?

That would be wonderful, but wouldn?t we need 20-odd folds to show it?

VII You wrote:

?7. Your forthcoming explanation "using reasoning based on the
behavior of the average slope Auq of c on (u,u^2) and the covariance
AubC of e and u in c on (u,e,u*e)" will probably go right over my
head, because I have only a hunch about what the average slope Auq
of c on (u,u^2) might mean, and not a clue about what the covariance
AubC of e and u in c on (u,e,u*e) might mean.?

I will hold off on this until I have read your response to my remarks
in (III) above. If the rules of the game have changed so that we
can?t use c on (u,u^2) IN CONCERT with c on (e,u,u*e), then I
obviously can?t base any argument on the behavior of the average slope
of the former when it?s regressed against available lengths and the
behavior of covariance of the latter (covariance of e and u) when it?s
regressed against available lengths. I have to be able to use both
behaviors to make the argument.

VIII. Thanks as always for your continued patience, tolerance, and
willingness to consider these matters.

Date Subject Author
11/21/12 Halitsky
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