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

Posted: Nov 29, 2012 11:29 AM
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Here are the SE?s for average slopes for a1_N_1_S and a1_N_1_C:

a1_N_1_S:

Len
ID obsN Avg Slope Avg slope SE

1 215 -4.805470268 0.950050755
2 314 -2.595530566 0.959429879
3 311 -2.291065716 1.024763870
4 210 -2.389119127 1.471966277
5 256 -1.215695376 1.398629841
6 246 -0.262323729 1.643926445
7 226 1.363522805 1.611512322
8 278 -0.560630170 1.620693559
9 246 2.374377463 1.847997565
10 211 -0.816451823 2.632764400
11 194 -0.499208768 2.855882984
12 234 1.968865343 2.864247061

a1_N_1_C:

Len
ID obsN Avg Slope Avg slope SE
1 166 -2.225882168 0.813316857
2 265 -2.315512399 0.693531939
3 258 -0.769858117 0.939333935
4 188 -1.697049757 1.291121211
5 243 -2.069842267 1.245969677
6 228 -4.427566827 1.508641800
7 219 -0.941379623 1.493402326
8 263 -2.069096413 1.534849449
9 233 -1.620229799 1.518979934
10 199 -3.764328472 2.294575586
11 185 -7.882327621 2.694025880
12 232 -11.82556530 3.055385684

You?ll see that:

a) for a1_N_1_S, going to the bounds implied by the SE will not change
the sign of the average slope only up to length interval 4 ? after
that the SE generally will;

b) for a1_N_1_C, the SE will only change the sign of the average slope
in two cases out of the 12: length intervals 3 and 7;

c) in both cases, SE increases considerably with length but ?much more
so? (?) for a1_N_1_C than for a1_N_1_S.

If it?s legit to draw conclusions from comparative behavior of SE?s in
contrasting sets of results like these, then interesting scientific
interpretations can be made of the above SE behaviors. But I?ve
learned not to jump the gun by making such interpretations based on
illegitimate interpretations of statistical behaviors. So, guidance
please, when you have a chance.

Also, regarding point (c) above, if it?s legitimate in general to look
at SE behavior in such results sets, is there a legitimate way to show
that the SE?s for a1_N_1_C really do increase significantly MORE with
increasing length interval than SE?s for a1_N_1_S? Or not? Again,
guidance please.

And thanks again as always for your continued consideration of these
matters.




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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