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Topic: The same four proportional weighting factors work for each
00/01/10/11 when 0.25 is subtracted from each !!!

Replies: 506   Last Post: Nov 20, 2012 9:21 PM

 Messages: [ Previous | Next ]
 Halitsky Posts: 600 Registered: 2/3/09
Re: 1) Sample "jackknife" table 2) Requisite n's 3) linear regression
comparisons; 4) sample equalization

Posted: May 24, 2012 12:02 PM

Thanks for the guidance on scaling the n0,n1?s (and also for the link
to the Kendall paper.)

Regarding your question about the ultimate test, I am going to give
you two answers, one short-winded and one long-winded. (But I think
tends to confirm your suspicion that the ?info? in the driver
correlations is in the variance of the residuals.)

Ultimate Test (Short-Winded)

Right now, the purpose of doing the logistic regressions is both
rhetorical and substantive.

For rhetorical purposes relative to getting out a paper, the results
of the logistic regressions comprise INITIAL HEURISTIC justification
for a deeper investigation into very novel idea that information in
protein message segments (info gained from the driver correlations)
can be used to predict alignability of substructures arising from
protein message segments (via info gained from the logistic
regressions.)

For substantive purposes, the results of the logistic regressions and
driver correlations contain all kinds of information that will be put
into a database for use in the actual ?ultimate tests? about which

In these ultimate tests, we will select pairs of protein message
segments completely at random, and attempt to predict whether they are
alignable via AML?s program, and if so, as members of what basic class
(a/alpha-helical, b(beta-sheet), c(mixed alpha-beta.) This is the set
of tests about which Arthur asked how you would see the role of false
positives/negatives in the design. If we do not have a method that is
able to use the information we?ve gathered from the regression
analyses to do this kind of ?de novo? blind prediction, then Arthur
doesn?t think we have much, in the final analysis. (But again,
results of such ?ultimate testing? would be presented in paper III,
after Papers I and II present the driver correlations and how they
drive the logistic regressions.)

Ultimate Test (Long-Winded)

You asked whether we could use other ?results? from Arthur?s program,
beyond the simple raw ?yields? reflected in the n0,n1 counts,
particularly results involving ?degree? of some parameter such as
lengths of substructures aligned, RMSD of alignment, etc.

I am more optimistic now that I was a month ago that this question can
be answered affirmatively, for the following reason.

For the sake of discussion, let?s restrict attention to segment data
obtained from the a1 fold for our 12 new length intervals using the
original (63,711) sets of study and control dicodons.

For these data, if you look at the CI?s of the slopes and intercepts
of the x1 and x2 driver correlations (as shown in the following four
tables), it is NOT immediately apparent how any logistic regression
model based on the x1,x2 predictors can possible yield different
results between control and study group, because with just a few
exceptions the CI?s for the study slopes overlap with the CI?s for the
control slopes, and same for the intercepts. And if the slopes and
intercepts of the x1 and x2 driver correlations can?t be said to
significantly differ between study and control groups, why should one
assume that these correlations should contain information useful to
the logistic regressions that we?ve based on the x1 and x2
predictors?

a1 Fold, (63,711) Dicodons, x1 driver lnc-lne on lnc -lnL

N Slope Study Control
i ln(GM) Stdy Cntl Stdy Cntl Low High Low High
1 3.237 227 230 1.42 1.15 1.25 1.60 1.06 1.23
2 3.237 313 384 1.35 1.10 1.20 1.49 1.04 1.17
3 3.554 309 347 1.42 1.07 1.26 1.57 0.99 1.15
4 3.699 218 248 1.22 1.09 1.04 1.40 1.01 1.18
5 3.848 254 289 1.25 1.11 1.08 1.42 1.03 1.19
6 3.987 241 260 1.38 1.27 1.18 1.58 1.18 1.36
7 4.117 167 189 1.00 1.08 0.67 1.34 0.94 1.22
8 4.247 238 284 1.25 1.16 1.08 1.42 1.08 1.23
9 4.374 227 233 1.46 1.31 1.22 1.69 1.19 1.43
10 4.503 191 201 1.62 1.26 1.37 1.88 1.11 1.40
11 4.633 168 171 1.56 1.35 1.29 1.83 1.20 1.49
12 4.760 209 210 1.60 1.30 1.36 1.84 1.17 1.42

a1 Fold, (63,711) Dicodons, x2 driver lnc-lnu on lnc -lnL

N Slope Study Control
i ln(GM) Stdy Cntl Stdy Cntl Low High Low High

1 3.237 227 230 1.46 0.87 1.18 1.75 0.78 0.96
2 3.237 313 384 1.27 0.89 1.03 1.52 0.82 0.96
3 3.554 309 347 1.07 0.93 0.81 1.33 0.86 0.99
4 3.699 218 248 1.15 1.02 0.87 1.44 0.98 1.07
5 3.848 254 289 1.04 0.97 0.74 1.33 0.92 1.02
6 3.987 241 260 1.01 0.99 0.72 1.30 0.94 1.05
7 4.117 167 189 0.90 0.97 0.45 1.36 0.89 1.05
8 4.247 238 284 0.86 1.04 0.57 1.16 0.98 1.09
9 4.374 227 233 0.89 0.98 0.48 1.29 0.91 1.06
10 4.503 191 201 0.87 0.98 0.52 1.23 0.91 1.05
11 4.633 168 171 0.73 0.97 0.31 1.15 0.89 1.04
12 4.760 209 210 0.75 0.95 0.36 1.15 0.88 1.02

a1 Fold, (63,711) Dicodons, x1 driver lnc-lne on lnc -lnL

N Inctpt Study Control
i ln(GM) Stdy Cntl Stdy Cntl Low High Low High

1 3.237 227 230 2.18 1.71 1.92 2.44 1.58 1.83
2 3.237 313 384 2.22 1.78 2.00 2.43 1.68 1.88
3 3.554 309 347 2.44 1.88 2.20 2.67 1.76 2.01
4 3.699 218 248 2.29 2.06 2.01 2.57 1.93 2.20
5 3.848 254 289 2.49 2.24 2.22 2.75 2.11 2.37
6 3.987 241 260 2.83 2.63 2.52 3.13 2.49 2.77
7 4.117 167 189 2.40 2.46 1.89 2.90 2.25 2.67
8 4.247 238 284 2.89 2.69 2.62 3.17 2.58 2.81
9 4.374 227 233 3.36 3.09 3.00 3.72 2.91 3.28
10 4.503 191 201 3.69 3.10 3.30 4.09 2.88 3.32
11 4.633 168 171 3.76 3.39 3.36 4.16 3.17 3.61
12 4.760 209 210 3.91 3.42 3.53 4.29 3.23 3.62

a1 Fold, (63,711) Dicodons, x2 driver lnc-lnu on lnc -lnL

N Inctpt Study Control
i ln(GM) Stdy Cntl Stdy Cntl Low High Low High

1 3.237 227 230 3.49 3.15 3.07 3.90 3.02 3.29
2 3.237 313 384 3.37 3.32 3.01 3.74 3.21 3.42
3 3.554 309 347 3.32 3.53 2.92 3.71 3.44 3.63
4 3.699 218 248 3.70 3.79 3.27 4.14 3.71 3.86
5 3.848 254 289 3.60 3.87 3.14 4.06 3.79 3.95
6 3.987 241 260 3.69 4.05 3.25 4.14 3.96 4.13
7 4.117 167 189 3.74 4.13 3.05 4.44 4.00 4.25
8 4.247 238 284 3.82 4.36 3.35 4.29 4.28 4.44
9 4.374 227 233 3.96 4.42 3.34 4.58 4.31 4.53
10 4.503 191 201 4.05 4.53 3.51 4.60 4.42 4.64
11 4.633 168 171 3.96 4.65 3.33 4.58 4.54 4.75
12 4.760 209 210 4.16 4.74 3.55 4.76 4.63 4.84

The answer, I think, is provided by the following two tables, which
make clear that the x1 and x2 driver correlations are significantly
different with respect to variance of residuals (when this difference
is gauged by Excel?s t-test ?assuming unequal variance?.)

[Note: in following two tables, "AAR" = "adjusted absolute residual"

a1 Fold, (63,711) Dicodons, x1 driver lnc-lne on lnc -lnL

N Mean AAR Var AAR 2-Tailed
i ln(GM) Stdy Cntl Stdy Cntl Study Cntl P

1 3.237 227 230 0.357 0.194 0.066 0.020 9.5E-16
2 3.237 313 384 0.329 0.172 0.060 0.012 6.7E-23
3 3.554 309 347 0.322 0.186 0.054 0.016 1.6E-18
4 3.699 218 248 0.323 0.167 0.054 0.012 2.1E-17
5 3.848 254 289 0.332 0.170 0.048 0.011 1.3E-23
6 3.987 241 260 0.327 0.158 0.051 0.011 5.9E-23
7 4.117 167 189 0.308 0.133 0.049 0.010 3.8E-18
8 4.247 238 284 0.244 0.116 0.038 0.007 5.6E-19
9 4.374 227 233 0.255 0.137 0.032 0.007 8.4E-18
10 4.503 191 201 0.276 0.158 0.033 0.010 5.4E-14
11 4.633 168 171 0.239 0.142 0.025 0.006 1.5E-11
12 4.760 209 210 0.237 0.126 0.034 0.007 9.4E-14
Correlns with ln(GM) -0.887 -0.800 -0.945 -0.842

a1 Fold, (63,711) Dicodons, x2 driver (lnc-lnu on lnc -lnL)

N Mean AAR Var AAR 2-Tailed
i ln(GM) Stdy Cntl Stdy Cntl Study Cntl P

1 3.237 227 230 0.525 0.155 0.226 0.043 3.8E-23
2 3.237 313 384 0.532 0.140 0.213 0.027 2.4E-37
3 3.554 309 347 0.494 0.114 0.205 0.017 1.5E-36
4 3.699 218 248 0.466 0.086 0.173 0.005 2.8E-30
5 3.848 254 289 0.530 0.093 0.185 0.007 1.0E-40
6 3.987 241 260 0.450 0.090 0.130 0.006 1.2E-37
7 4.117 167 189 0.424 0.075 0.091 0.004 9.1E-33
8 4.247 238 284 0.430 0.077 0.104 0.004 7.7E-43
9 4.374 227 233 0.446 0.077 0.090 0.003 2.0E-47
10 4.503 191 201 0.384 0.076 0.058 0.003 8.4E-42
11 4.633 168 171 0.370 0.061 0.062 0.002 7.4E-36
12 4.760 209 210 0.410 0.066 0.064 0.003 1.9E-49
Correlns with ln(GM) -0.891 -0.915 -0.965 -0.812

Not only do the above two tables indicate that the x1 and x2 driver
correlations differ significantly with respect to variance of
residuals, but they also indicate that in both cases, variance of
residuals inversely correlates strongly with segment length.

And it is this new correlation between residual variance and length
which gives me hope that we can tie residual variance to one or more
"degree"-type results from Arthur's programs, since there are two or
three, if not more, such results that will more than likely vary with
length as well.

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10/12/12 Ray Koopman
10/12/12 Halitsky
10/12/12 Halitsky
10/12/12 Ray Koopman
10/12/12 Halitsky
10/12/12 Ray Koopman
10/12/12 Halitsky
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9/21/12 Halitsky
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8/25/12 Halitsky
8/26/12 Ray Koopman
8/26/12 Halitsky
8/26/12 Halitsky
8/27/12 Ray Koopman
8/27/12 Halitsky
8/27/12 Halitsky
8/28/12 Halitsky
8/28/12 Halitsky
8/31/12 Halitsky
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7/25/12 Halitsky
6/27/12 Halitsky
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6/22/12 Halitsky
6/22/12 Halitsky
6/2/12 Halitsky
6/3/12 Ray Koopman
5/30/12 Halitsky
5/30/12 Ray Koopman
5/30/12 Halitsky
5/30/12 Halitsky
5/26/12 Halitsky
5/26/12 Halitsky
5/26/12 Ray Koopman
5/26/12 Halitsky
5/27/12 Ray Koopman
5/25/12 Halitsky
5/25/12 Halitsky
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5/20/12 Ray Koopman
5/20/12 Halitsky
5/20/12 Ray Koopman
5/20/12 Halitsky
5/15/12 Ray Koopman
5/15/12 Halitsky