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

Posted: Nov 27, 2012 9:19 AM
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1.

You wrote:

?slope = dy/dx = a1 + 2*a2*x?

Oh! That slope! (Of the tangent to the quadratic at x = 0.) Duh!

I was construing ?slope? as just a alternative term for ?coefficient?
? don?t know why. Someday I?ll learn if that if I can?t make sense of
something you?ve written, then I?ve construed something wrongly.

2.

When I re-run the analysis, I will use (u/1+u) instead of u. So I
assume I would use ln(u/(1+u)), and (ln(u+(1/u)))^2, parallel to ln(u)
and (ln(u))^2? (Unless you don?t want me to take logs ? please
clarify here.)

3. You wrote:

?For instance, you might get the slope at each data point and then use
their literal average, a1 + 2*a2*mean_x. But what if cells with
different x-means give the same a1 and a2? Should their
"average slope" measures be the same or different? That's the kind of
question you have to ask yourself.?

Since I can?t think that far ahead in the abstract (as you can), I
will use ?a1 + 2*a2*mean_x? initially, and see if any peculiarities
arise of the sort you mention (or others.)

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
the other thread:

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:

Bonferronu 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.



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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