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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

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Halitsky

Posts: 600
Registered: 2/3/09
Re linearity of the Axxxx SE plots – hold on to yo
ur hat

Posted: Dec 14, 2012 4:07 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In your post of 12/14 at227 pm, you wrote:

?So far the all the plots look pretty linear, with just a hint of
positive curvature, but it's hard to say because SEs are themselves
heteroscedastic.?

The Axxxx SEplots I?m going to send at set 2 and set 3 may be relevant
to this matter, for the reason(s) below.

As soon as I started the Axxxx SE plots for set 2 (none of which
you?ve yet received), I immediately saw something which you can see
for yourself by plotting the two tables at the end of this post, which
are for:

a) N_1_a1_S (you already have the plot for this one)
b) N_2_a1_S (haven?t sent this one to you yet)

So, as you review the set 2 plots I?m going to start sending you now,
please keep an eye out to see whether you think that each new set 2
plot and its corresponding set 1 plot differ in the same way as the
plots from the two tables below. If they do, then we may have quite a
story to tell about the evolution of the a1 hemoglobins, depending
additionally on how the plots pattern at set 3.

Also, one methodological point is worth mentioning ? it may well be
that we have to use different sets at different lengths in order to
get the most predictive results from our regressions. This is
something that has never occurred to me before, but it makes perfect
sense if there is any merit to of the ?evolutionary story? that we may
be privileged to watch unfold as we step through the set 2 and set 3
plots for the Axxxx SE?s ...

Here are the two tables:

N_1_a1_S for AuqSE

LenID,AuqSE
24,2.391090499
25,1.970272847
26,1.833852826
27,1.627804729
28,1.660754005
29,2.100638906
30,2.095449739
31,2.741154079
32,2.882615934
33,2.046833808
34,2.330966524
35,2.345954541
36,2.347776152
37,2.38379688
38,3.316455252
39,4.216434186
40,2.968687167
41,4.142953247
42,2.944999077
43,4.495050552
44,4.272428433
45,3.701894193
46,3.943947579
47,3.851746773
48,3.518900664
49,3.270414279
50,3.799579601
51,4.589503931
52,3.706371331
53,6.196501544
54,4.204274757
55,4.420960299
56,4.142962385
57,3.817171845
58,6.906216774
59,7.956243823
60,2.854383526
61,3.521807881
62,4.620311737
63,4.468918831
64,4.396886144
65,3.808878305
66,3.867478161
67,4.254578321
68,4.839232026
69,3.49155102
70,4.387907593
71,6.478845422
72,4.211951915
73,6.040173708
74,8.259278149
75,5.726134066
76,5.473975542
77,5.104227158
78,5.432747382
79,5.90339531
80,4.561326404
81,4.70453793
82,7.642736138
83,7.371524379
84,6.050326507
85,11.51203861
86,8.080943039
87,14.92212195
88,5.877460304
89,13.79719486
90,13.26087283
91,6.74533113
92,9.99828549
93,8.519877424
94,7.548529057
95,14.10284784
96,16.29681278
97,10.70332106
98,16.23766271
99,7.295347809
100,6.860653359
101,7.480988142
102,9.215511046
103,13.77380369
104,10.66342047
105,16.06223739
106,10.25084926
107,17.33622667
108,6.683281478
109,10.64821667
110,8.261818482
111,18.03621053
112,8.203764319
113,10.4479606
114,15.00264375
115,7.103613139
116,6.062510063
117,14.83693648
118,23.74404795
119,11.8211972
120,8.007851245
121,16.36658664
122,11.82042482
123,6.576225902
124,7.97205398

N_2_a1_S for AuqSE
LenID,AuqSE
24,2.009510899
25,2.079532091
26,2.005311512
27,2.065102106
28,1.79708132
29,2.25021611
30,2.023803981
31,3.104929517
32,2.725543284
33,2.277963818
34,2.693343371
35,2.765368032
36,2.810260396
37,2.871219663
38,2.887943477
39,3.2552243
40,3.424801687
41,4.082266916
42,3.940772349
43,4.327475125
44,4.333196572
45,3.923964932
46,4.364002233
47,3.128401813
48,4.125673988
49,4.898836764
50,4.038263422
51,4.510564961
52,4.366261094
53,4.570148472
54,5.114817395
55,5.090364099
56,4.964979812
57,4.572620636
58,4.342199195
59,4.342526169
60,5.367979026
61,3.815912772
62,4.404916381
63,5.555182799
64,7.83624113
65,6.038510007
66,5.500534573
67,6.113190178
68,8.994647295
69,6.008023666
70,5.452987842
71,6.547399574
72,6.909605179
73,5.44707708
74,6.861502505
75,7.913779537
76,8.763370263
77,7.579007665
78,7.236166753
79,6.521927747
80,6.780374612
81,9.793383281
82,7.415349337
83,9.751480335
84,9.29584359
85,8.956051219
86,16.53304959
87,10.06962341
88,8.356779285
89,7.845313074
90,5.865301697
91,8.538208941
92,9.855107209
93,8.368842383
94,9.017658787
95,6.537178028
96,6.261494533
97,6.021414213
98,9.947415174
99,9.989875204
100,8.669174851
101,10.06496757
102,11.71200846
103,12.02642726
104,11.31683809
106,9.313690275
107,10.91630402
109,10.45031468
115,10.93027511



Date Subject Author
11/21/12
Read Interpretation of coefficients in multiple regressions which model
linear dependence on an IV
Halitsky
11/21/12
Read The problematic regression is actually ln(c) on ( ln(u), ln(u^2) ),
not c on (u, u^2)
Halitsky
11/22/12
Read Re: The problematic regression is actually ln(c) on ( ln(u), ln(u^2)
), not c on (u, u^2)
Ray Koopman
11/22/12
Read Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Halitsky
11/23/12
Read Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Ray Koopman
11/23/12
Read Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)
Halitsky
11/23/12
Read Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Halitsky
11/24/12
Read Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Ray Koopman
11/24/12
Read Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions
Halitsky
11/24/12
Read You now have N_1_S, N_2_S, and N_3_S files for all folds
Halitsky
11/25/12
Read As per your suggestion in the other thread, scaled e on scaled u, c, L
Halitsky
11/26/12
Read Re: As per your suggestion in the other thread, scaled e on scaled u,
c, L
Ray Koopman
11/26/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
11/26/12
Read Them there is some neat algebraic mechanics !
Halitsky
11/27/12
Read Re: Them there is some neat algebraic mechanics !
Ray Koopman
11/27/12
Read OK – I think I’m set, at least till we get to c
on (e, u, u*e).
Halitsky
11/27/12
Read Re: OK – I think I’m set, at least till we get t
o c on (e, u, u*e).
Ray Koopman
11/28/12
Read Re: OK – I think I’m set, at least till we get t
o c on (e, u, u*e).
Ray Koopman
11/28/12
Read Thanks for your review of Tables I/II from previous analysis
Halitsky
11/27/12
Read Holy Cow! Look at your "average a1" slope regressed on Len Int
Halitsky
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Ray Koopman
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Halitsky
11/27/12
Read Re: Holy Cow! Look at your "average a1" slope regressed on Len Int
Ray Koopman
11/27/12
Read Here's how I did logs ...
Halitsky
11/27/12
Read Please note that $u = u in last post (the $ prefix is from PERL - sorry).
Halitsky
11/27/12
Read Re: Here's how I did logs ...
Ray Koopman
11/28/12
Read Average slopes and means of u' for c on (u',u'^2) WITHOUT logs
Halitsky
11/28/12
Read Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)
Halitsky
11/28/12
Read Re: Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)
Ray Koopman
11/28/12
Read Finally! Pay-off for all that work I did with the "A" matrix returned
by Ivor Welch's module!
Halitsky
11/29/12
Read Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Halitsky
11/30/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)
Ray Koopman
12/2/12
Read Glad you brought up “singleton” length intervals
... been thinkin’ on ‘em also ...
Halitsky
12/2/12
Read Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...
Ray Koopman
12/2/12
Read It's still 24...124 - don't know why I bothered to say "roughly
25...125" instead of "exactly "24...124"
Halitsky
12/2/12
Read You should probably clear your data deck and start fresh with the two
csv's I just mentioned in the last email
Halitsky
12/2/12
Read Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...
Halitsky
12/2/12
Read One last thought: definitions for the third regression (will save a
complete re-run if I incorporate them now) ...
Halitsky
12/3/12
Read Number of Bonferroni entries for each singleton length is still 72 (duh!)
Halitsky
11/30/12
Read En passant question: What if a plot of slope CI’s
is lousy, but splits the “m’s” perfectly?
Halitsky
11/30/12
Read Re: En passant question: What if a plot of slope CI
’s is lousy, but splits the “m’s” perfectly?
Ray Koopman
12/1/12
Read I’m glad the perfect m split legitimately suggests
a subset effect; here’s why.
Halitsky
12/1/12
Read Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.
Ray Koopman
12/1/12
Read Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.
Halitsky
12/1/12
Read Slope and intercept for R'uq in the above example ...
Halitsky
12/1/12
Read Bonferroni tables for p’s from new 2-ways for Auq
per fold and length interval
Halitsky
12/1/12
Read Nope! 24-entry Bonferroni tables for (a1,a3) and (b1,b47) do NOT
improve results for a3 nor b47
Halitsky
12/5/12
Read I'm VERY glad you'll know how to answer this "perms and combs"
question !
Halitsky
12/5/12
Read “L-H Het” Table for Average Slopes Auq, Aubu, Au
bqu
Halitsky
12/5/12
Read In "L-H Het table", L-H Het for N1 Aubu should be 4, NOT 2
Halitsky
12/5/12
Read Holy Moly, were you right about covariances for Rub and Rubq !!!!
Halitsky
12/5/12
Read Re: Holy Moly, were you right about covariances for Rub and Rubq !!!!
Ray Koopman
12/6/12
Read So do we need to "Bonferroni-correct" in this case
Halitsky
12/7/12
Read Re: So do we need to "Bonferroni-correct" in this case
Ray Koopman
12/7/12
Read Response to your last of 12/7 at 12:17am
Halitsky
12/7/12
Read Re: Response to your last of 12/7 at 12:17am
Ray Koopman
12/7/12
Read Thanks for the guidance on how to evaluate the contribution of u^2 in
the second model.
Halitsky
12/7/12
Read Please ignore my first question about "estimated standard errpr" in
my last post !!!! Sorry !
Halitsky
12/7/12
Read The u^2 coefficient in c on (e,u,u*e,u^2) does NOT distinguish among
the four subset x MoSS roll-ups
Halitsky
12/7/12
Read Sorry! Those were the SE's in my last post, not the t's !
Halitsky
12/7/12
Read SE's and p's for four subset x MoSS roll-ups of u*e coefficient in c
= (u,e,u*e)
Halitsky
12/7/12
Read Re: SE's and p's for four subset x MoSS roll-ups of u*e coefficient
in c = (u,e,u*e)
Ray Koopman
12/7/12
Read I'm sorry Ray - excitement (probably unwarranted) has disconnected my
brain from my fingers ...
Halitsky
12/7/12
Read Must we say S,N instead of N,S if we've said "Subset x MoSS" (not
MoSS x Subset) ???
Halitsky
12/7/12
Read Re: Must we say S,N instead of N,S if we've said "Subset x MoSS" (not
MoSS x Subset) ???
Ray Koopman
12/7/12
Read Response to your last
Halitsky
12/8/12
Read Re: Response to your last
Ray Koopman
12/8/12
Read Re: Response to your last
Ray Koopman
12/8/12
Read I think I understand; if so, then here’s what I ex
pect you’ll agree I should do next
Halitsky
12/9/12
Read Thanks so much for the sample picture you sent off-line
Halitsky
12/8/12
Read One other thing - because we're using "c-average", not "c-simple",
"c" is no longer a pure count
Halitsky
12/8/12
Read One other possibly worthwhile observation regarding the term u*e in
the regression c on (e,u,u^e,u^2)
Halitsky
12/8/12
Read Typo's of u^e for u*e in previous post.
Halitsky
12/9/12
Read Could I impose on you for four more ordered p “ref
erence plots”?
Halitsky
12/9/12
Read Have sent off-line a PDF of the four plots themselves graphed all together.
gimpeltf@hotmail.com
12/9/12
Read I'm getting the hang of the plotting now - see PDF SNa1_1_for_Rubq
sent offline
Halitsky
12/9/12
Read Am resending the last PDF sent off-line, since I've now learned how
to highlight the line of interest against the random backdrop.
Halitsky
12/10/12
Read Re: Am resending the last PDF sent off-line, since I've now learned
how to highlight the line of interest against the random backdrop.
Ray Koopman
12/10/12
Read 1) Just u*e and u^2(!!); 2) IOTs vs “proper” tes
ts
Halitsky
12/10/12
Read Re: 1) Just u*e and u^2(!!); 2) IOTs vs “proper”
tests
Ray Koopman
12/10/12
Read Response to your last re Q and p
Halitsky
12/10/12
Read Sorry! I meant set=2, not set =1 in last post ...
Halitsky
12/11/12
Read Re: Response to your last re Q and p
Ray Koopman
12/11/12
Read 1) yes - I am using abs(t); 2) subtraction from 1
Halitsky
12/10/12
Read Results of p's obtained by referring Q’s to the ch
i-square distribution.
Halitsky
12/11/12
Read Correction to harmless "thought-typo" in last post
Halitsky
12/11/12
Read Another way to bring the other folds in might be via investigation of
your average slopes and covar vis a vis "hetness"
Halitsky
12/11/12
Read Re: Results of p's obtained by referring Q’s to th
e chi-square distribution.
Ray Koopman
12/11/12
Read OK then, how ‘bout “hetness”? Are you amenabl
e to its further investigation?
Halitsky
12/12/12
Read Re: OK then, how ‘bout “hetness”? Are you amen
able to its further investigation?
Ray Koopman
12/12/12
Read I need to correct an apparent miscommunication regar
ding derivation of het H’s and L’s
Halitsky
12/13/12
Read Re: I need to correct an apparent miscommunication r
egarding derivation of het H’s and L’s
Ray Koopman
12/13/12
Read The SE's are in the zipped files but here they are for your
convenience ....
Halitsky
12/13/12
Read Re: The SE's are in the zipped files but here they are for your
convenience ....
Ray Koopman
12/13/12
Read Re your question about "linearity of SE’s in lengt
h"
Halitsky
12/14/12
Read Re: Re your question about "linearity of SE’s in l
ength"
Ray Koopman
12/14/12
Read Your question re features of (L,Aubqe) plots
Halitsky
12/13/12
Read I think I may have found something relevant to Aubqe
“het-ness” and heteroscedasticity
Halitsky
12/13/12
Read Re: I think I may have found something relevant to A
ubqe “het-ness” and heteroscedasticity
Ray Koopman
12/14/12
Read Re your questions about the plots sent off-line (and the underlying
data posted here 12/13 at 10:33am)
Halitsky
12/14/12
Read Re: Re your questions about the plots sent off-line (and the
underlying data posted here 12/13 at 10:33am)
Ray Koopman
12/14/12
Read Thanks for the terminological/methodological corrections, and also
for the ref to gnuplot.
Halitsky
12/14/12
Read Re: Thanks for the terminological/methodological corrections, and
also for the ref to gnuplot.
Ray Koopman
12/14/12
Read Response to your last of 12/14 at 227pm re terminology and methodology.
Halitsky
12/14/12
Read Re linearity of the Axxxx SE plots – hold on to yo
ur hat
Halitsky
12/14/12
Read Re: Re linearity of the Axxxx SE plots – hold on t
o your hat
Ray Koopman
12/14/12
Read Thanks for doing those two plots - yes - we agree on what we're seeing
Halitsky
12/14/12
Read Re: Thanks for doing those two plots - yes - we agree on what we're seeing
Ray Koopman
12/15/12
Read Re: Thanks for doing those two plots - yes - we agree on what we're seeing
Ray Koopman
12/15/12
Read Re plot of SEP against L
Halitsky
12/15/12
Read Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm
Halitsky
12/15/12
Read Re: Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm
Ray Koopman
12/14/12
Read One other general question regarding scaling to [0,1].
Halitsky
12/14/12
Read Re: One other general question regarding scaling to [0,1].
Ray Koopman
12/14/12
Read Sorry - I will be typographically more careful re Aubqe in the future.
Halitsky
12/1/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/1/12
Read Thanks for elucidation of 2nd new regression.
Halitsky
12/1/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/1/12
Read Roger corrected defs; also, will add new cov, just in case it's
needed later
Halitsky
12/2/12
Read Re: Interpretation of coefficients in multiple regressions which
model linear dependence on an IV
Ray Koopman
12/2/12
Read 1) thanks for the 3rd regression defs; 2) Yes - I see why the terms
aren't "symmetrical" in this case.
Halitsky
12/3/12
Read New copies of a1_N_1_C and a1_N_1_S with data for all three
regressions at each singleton length.
Halitsky
12/3/12
Read Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Halitsky
12/3/12
Read Have sent off-line all N_1 regression coefficient files and master N
per length index file for N1
Halitsky
12/3/12
Read Same as above post for f_N_2_ss
Halitsky
12/3/12
Read Same as above post for f_N_3_ss
Halitsky
12/3/12
Read Same as above post for f_R_1_ss
Halitsky
12/3/12
Read Same as above post for f_R_2_ss
Halitsky
12/3/12
Read Same as above post for f_R_3_ss
Halitsky
12/3/12
Read Re: Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Ray Koopman
12/4/12
Read Sparseness of b1 data ...
Halitsky
12/4/12
Read I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3
Halitsky
12/4/12
Read Re: I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3
Ray Koopman
12/4/12
Read No - the counts in the files themselves are all OK.
Halitsky
12/4/12
Read Re: Sparseness of b1 data ...
Ray Koopman
12/5/12
Read We cross posted, so I just saw your revised "counts" table after I
made my last two posts ...
Halitsky
12/4/12
Read Let me know if you're ready for some interesting data, or if you're
too busy analyzing
Halitsky
12/4/12
Read Re: Let me know if you're ready for some interesting data, or if
you're too busy analyzing
Ray Koopman
12/4/12
Read Please evaluate this "yield" table of method/subset avg slope 2-ways
per fold and len with p < .05
Halitsky
12/5/12
Read One other question about using Auq avg slope as a constant when
computing the other two regressions
Halitsky
12/5/12
Read Re: One other question about using Auq avg slope as a constant when
computing the other two regressions
Ray Koopman
12/5/12
Read Re: One other question about using Auq avg slope as a constant when
computing the other two regressions
Halitsky
12/4/12
Read Some of your counts apparently ARE off.
Halitsky
12/4/12
Read Sorry! those counts in my last post were for len 63 in b1 (forgot to
tell you the length!!!!)
Halitsky
12/4/12
Read Re: Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell
Ray Koopman

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