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Math Forum » Discussions » sci.math.* » sci.stat.math.independent

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

Average slopes and means of u' for c on (u',u'^2) WITHOUT logs
Posted: Nov 28, 2012 10:17 AM

Plain Text

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For the regression Ruq = c on (u',u'^2) where u' = u/(1+u), here are
the values of the average slopes and means of u' for all 12 length
intervals of a1_N_1_S:

Len
Int Avg Slope Mean u'

1 -4.805470268 0.598938454
2 -2.595530566 0.600488771
3 -2.291065716 0.583140716
4 -2.389119127 0.557133081
5 -1.215695376 0.576625407
6 -0.262323729 0.573183536
7 1.363522805 0.553100523
8 -0.560630170 0.553945343
9 2.374377463 0.559499755
10 -0.816451823 0.569038015
11 -0.499208768 0.569087642
12 1.968865343 0.558095787

The regression of average slope on LenInt is slightly better WITHOUT
logs.

But note that corresponding to the fairly strong direct correlation of
AvgSlope wiht LenInt, there is ALSO a fairly strong inverse
correlation of Mean(u') with LenInt.

I THINK this result means that at least in this case, your current
definition of average slope is "OK", because the means are varying
systematically, not arbitrarily at my "whim", to use your piquant
expression.

But I'm not at all sure of this conclusion, so I'm anxious to get your
evaluation of this situation. Is your definition of average slope
"OK" or not?

Or can you not tell until I?ve obtained the data for all the cells of
the current model? (Note: ?current? here means without uL/uH
dichotomy.)

Date

Subject

Author

11/21/12

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

Halitsky

11/21/12

The problematic regression is actually ln(c) on ( ln(u), ln(u^2) ),
not c on (u, u^2)

Halitsky

11/22/12

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

Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)

Halitsky

11/23/12

Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)

Ray Koopman

11/23/12

Re: Off-line Zip File with one Summ File and 12 Detl files for lnc on (lnu,(lnu)^2)

Halitsky

11/23/12

Complete "a1_N_1_S" zipfile with results from all 3 new regressions

Halitsky

11/24/12

Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions

Ray Koopman

11/24/12

Re: Complete "a1_N_1_S" zipfile with results from all 3 new regressions

Halitsky

11/24/12

You now have N_1_S, N_2_S, and N_3_S files for all folds

Halitsky

11/25/12

As per your suggestion in the other thread, scaled e on scaled u, c, L

Halitsky

11/26/12

Re: As per your suggestion in the other thread, scaled e on scaled u,
c, L

Ray Koopman

11/26/12

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

Ray Koopman

11/26/12

Them there is some neat algebraic mechanics !

Halitsky

11/27/12

Re: Them there is some neat algebraic mechanics !

Ray Koopman

11/27/12

OK – I think I’m set, at least till we get to c
on (e, u, u*e).

Halitsky

11/27/12

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

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

Thanks for your review of Tables I/II from previous analysis

Halitsky

11/27/12

Holy Cow! Look at your "average a1" slope regressed on Len Int

Halitsky

11/27/12

Re: Holy Cow! Look at your "average a1" slope regressed on Len Int

Ray Koopman

11/27/12

Re: Holy Cow! Look at your "average a1" slope regressed on Len Int

Halitsky

11/27/12

Re: Holy Cow! Look at your "average a1" slope regressed on Len Int

Ray Koopman

11/27/12

Here's how I did logs ...

Halitsky

11/27/12

Please note that $u = u in last post (the $ prefix is from PERL - sorry).

Halitsky

11/27/12

Re: Here's how I did logs ...

Ray Koopman

11/28/12

Average slopes and means of u' for c on (u',u'^2) WITHOUT logs

Halitsky

11/28/12

Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)

Halitsky

11/28/12

Re: Results (!!) on average slopes and means for a1_N_1_C (complement
instead of core subset)

Ray Koopman

11/28/12

Finally! Pay-off for all that work I did with the "A" matrix returned
by Ivor Welch's module!

Halitsky

11/29/12

Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)

Halitsky

11/30/12

Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)

Ray Koopman

12/2/12

Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)

Ray Koopman

12/2/12

Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)

Ray Koopman

12/2/12

Glad you brought up “singleton” length intervals
... been thinkin’ on ‘em also ...

Halitsky

12/2/12

Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...

Ray Koopman

12/2/12

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

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

Re: Glad you brought up “singleton” length inter
vals ... been thinkin’ on ‘em also ...

Halitsky

12/2/12

One last thought: definitions for the third regression (will save a
complete re-run if I incorporate them now) ...

Halitsky

12/3/12

Number of Bonferroni entries for each singleton length is still 72 (duh!)

Halitsky

11/30/12

En passant question: What if a plot of slope CI’s
is lousy, but splits the “m’s” perfectly?

Halitsky

11/30/12

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

I’m glad the perfect m split legitimately suggests
a subset effect; here’s why.

Halitsky

12/1/12

Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.

Ray Koopman

12/1/12

Re: I’m glad the perfect m split legitimately sugg
ests a subset effect; here’s why.

Halitsky

12/1/12

Slope and intercept for R'uq in the above example ...

Halitsky

12/1/12

Bonferroni tables for p’s from new 2-ways for Auq
per fold and length interval

Halitsky

12/1/12

Nope! 24-entry Bonferroni tables for (a1,a3) and (b1,b47) do NOT
improve results for a3 nor b47

Halitsky

12/5/12

I'm VERY glad you'll know how to answer this "perms and combs"
question !

Halitsky

12/5/12

“L-H Het” Table for Average Slopes Auq, Aubu, Au
bqu

Halitsky

12/5/12

In "L-H Het table", L-H Het for N1 Aubu should be 4, NOT 2

Halitsky

12/5/12

Holy Moly, were you right about covariances for Rub and Rubq !!!!

Halitsky

12/5/12

Re: Holy Moly, were you right about covariances for Rub and Rubq !!!!

Ray Koopman

12/6/12

So do we need to "Bonferroni-correct" in this case

Halitsky

12/7/12

Re: So do we need to "Bonferroni-correct" in this case

Ray Koopman

12/7/12

Response to your last of 12/7 at 12:17am

Halitsky

12/7/12

Re: Response to your last of 12/7 at 12:17am

Ray Koopman

12/7/12

Thanks for the guidance on how to evaluate the contribution of u^2 in
the second model.

Halitsky

12/7/12

Please ignore my first question about "estimated standard errpr" in
my last post !!!! Sorry !

Halitsky

12/7/12

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

Sorry! Those were the SE's in my last post, not the t's !

Halitsky

12/7/12

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

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

I'm sorry Ray - excitement (probably unwarranted) has disconnected my
brain from my fingers ...

Halitsky

12/7/12

Must we say S,N instead of N,S if we've said "Subset x MoSS" (not
MoSS x Subset) ???

Halitsky

12/7/12

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

Response to your last

Halitsky

12/8/12

Re: Response to your last

Ray Koopman

12/8/12

Re: Response to your last

Ray Koopman

12/8/12

I think I understand; if so, then here’s what I ex
pect you’ll agree I should do next

Halitsky

12/9/12

Thanks so much for the sample picture you sent off-line

Halitsky

12/8/12

One other thing - because we're using "c-average", not "c-simple",
"c" is no longer a pure count

Halitsky

12/8/12

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

Typo's of u^e for u*e in previous post.

Halitsky

12/9/12

Could I impose on you for four more ordered p “ref
erence plots”?

Halitsky

12/9/12

Have sent off-line a PDF of the four plots themselves graphed all together.

gimpeltf@hotmail.com

12/9/12

I'm getting the hang of the plotting now - see PDF SNa1_1_for_Rubq
sent offline

Halitsky

12/9/12

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

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

1) Just u*e and u^2(!!); 2) IOTs vs “proper” tes
ts

Halitsky

12/10/12

Re: 1) Just u*e and u^2(!!); 2) IOTs vs “proper”
tests

Ray Koopman

12/10/12

Response to your last re Q and p

Halitsky

12/10/12

Sorry! I meant set=2, not set =1 in last post ...

Halitsky

12/11/12

Re: Response to your last re Q and p

Ray Koopman

12/11/12

1) yes - I am using abs(t); 2) subtraction from 1

Halitsky

12/10/12

Results of p's obtained by referring Q’s to the ch
i-square distribution.

Halitsky

12/11/12

Correction to harmless "thought-typo" in last post

Halitsky

12/11/12

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

Re: Results of p's obtained by referring Q’s to th
e chi-square distribution.

Ray Koopman

12/11/12

OK then, how ‘bout “hetness”? Are you amenabl
e to its further investigation?

Halitsky

12/12/12

Re: OK then, how ‘bout “hetness”? Are you amen
able to its further investigation?

Ray Koopman

12/12/12

I need to correct an apparent miscommunication regar
ding derivation of het H’s and L’s

Halitsky

12/13/12

Re: I need to correct an apparent miscommunication r
egarding derivation of het H’s and L’s

Ray Koopman

12/13/12

The SE's are in the zipped files but here they are for your
convenience ....

Halitsky

12/13/12

Re: The SE's are in the zipped files but here they are for your
convenience ....

Ray Koopman

12/13/12

Re your question about "linearity of SE’s in lengt
h"

Halitsky

12/14/12

Re: Re your question about "linearity of SE’s in l
ength"

Ray Koopman

12/14/12

Your question re features of (L,Aubqe) plots

Halitsky

12/13/12

I think I may have found something relevant to Aubqe
“het-ness” and heteroscedasticity

Halitsky

12/13/12

Re: I think I may have found something relevant to A
ubqe “het-ness” and heteroscedasticity

Ray Koopman

12/14/12

Re your questions about the plots sent off-line (and the underlying
data posted here 12/13 at 10:33am)

Halitsky

12/14/12

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

Thanks for the terminological/methodological corrections, and also
for the ref to gnuplot.

Halitsky

12/14/12

Re: Thanks for the terminological/methodological corrections, and
also for the ref to gnuplot.

Ray Koopman

12/14/12

Response to your last of 12/14 at 227pm re terminology and methodology.

Halitsky

12/14/12

Re linearity of the Axxxx SE plots – hold on to yo
ur hat

Halitsky

12/14/12

Re: Re linearity of the Axxxx SE plots – hold on t
o your hat

Ray Koopman

12/14/12

Thanks for doing those two plots - yes - we agree on what we're seeing

Halitsky

12/14/12

Re: Thanks for doing those two plots - yes - we agree on what we're seeing

Ray Koopman

12/15/12

Re: Thanks for doing those two plots - yes - we agree on what we're seeing

Ray Koopman

12/15/12

Re plot of SEP against L

Halitsky

12/15/12

Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm

Halitsky

12/15/12

Re: Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm

Ray Koopman

12/14/12

One other general question regarding scaling to [0,1].

Halitsky

12/14/12

Re: One other general question regarding scaling to [0,1].

Ray Koopman

12/14/12

Sorry - I will be typographically more careful re Aubqe in the future.

Halitsky

12/1/12

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

Ray Koopman

12/1/12

Thanks for elucidation of 2nd new regression.

Halitsky

12/1/12

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

Ray Koopman

12/1/12

Roger corrected defs; also, will add new cov, just in case it's
needed later

Halitsky

12/2/12

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

Ray Koopman

12/2/12

1) thanks for the 3rd regression defs; 2) Yes - I see why the terms
aren't "symmetrical" in this case.

Halitsky

12/3/12

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

Since 3rd regression computation needs df = 5, am requiring 15
observations for any given length singleton in any cell

Halitsky

12/3/12

Have sent off-line all N_1 regression coefficient files and master N
per length index file for N1

Halitsky

12/3/12

Same as above post for f_N_2_ss

Halitsky

12/3/12

Same as above post for f_N_3_ss

Halitsky

12/3/12

Same as above post for f_R_1_ss

Halitsky

12/3/12

Same as above post for f_R_2_ss

Halitsky

12/3/12

Same as above post for f_R_3_ss

Halitsky

12/3/12

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

Sparseness of b1 data ...

Halitsky

12/4/12

I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3

Halitsky

12/4/12

Re: I realized I should clarify my 4-way b1 match table: it's AFTER
subtracting df of 3

Ray Koopman

12/4/12

No - the counts in the files themselves are all OK.

Halitsky

12/4/12

Re: Sparseness of b1 data ...

Ray Koopman

12/5/12

We cross posted, so I just saw your revised "counts" table after I
made my last two posts ...

Halitsky

12/4/12

Let me know if you're ready for some interesting data, or if you're
too busy analyzing

Halitsky

12/4/12

Re: Let me know if you're ready for some interesting data, or if
you're too busy analyzing

Ray Koopman

12/4/12

Please evaluate this "yield" table of method/subset avg slope 2-ways
per fold and len with p < .05

Halitsky

12/5/12

One other question about using Auq avg slope as a constant when
computing the other two regressions

Halitsky

12/5/12

Re: One other question about using Auq avg slope as a constant when
computing the other two regressions

Ray Koopman

12/5/12

Re: One other question about using Auq avg slope as a constant when
computing the other two regressions

Halitsky

12/4/12

Some of your counts apparently ARE off.

Halitsky

12/4/12

Sorry! those counts in my last post were for len 63 in b1 (forgot to
tell you the length!!!!)

Halitsky

12/4/12

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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