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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

 Messages: [ Previous | Next ]
 Halitsky Posts: 600 Registered: 2/3/09
I’m glad the perfect m split legitimately suggests
a subset effect; here’s why.

Posted: Dec 1, 2012 1:15 AM

(I) Further suggestive CI plot evidence for a subset effect.

?so it certainly looks like there's a subset effect.?

because the postulation of such an effect is supported by additional
CI plot evidence that I?ll get to in a moment.

But first, I want to clarify what CI?s and slopes we?re talking about
here.

Denote the first of the three new reqressions by Ruq:

Ruq = c on (u?, (u?)^2), where u?= u/(1+u)

with average slope Auq = first derivative of the quadratic (as you
defined it) and SE of average slope also as you defined it:
sqrt[ var(a1) + 4*var(a2)*(mean_x)^2 + 4*cov(a1,a2)*mean_x ], with df
= n-3. (Note that Ruq is always executed per length interval per fold
per dicodon subset per dicodon set per ?method?, where ?method? is
your term for N=nonrandom vs R=random.)

Now define R?uq as the simple linear regression:

R?uq = Auq on the index values 1-12 of our length intervals.

where R?uq is always performed per fold, dicodon set, dicodon subset,
and method

Then inasmuch as the plot you just examined graphically exhibits the
slopes and CI?s for the executions of R?uq in the twelve cells defined
by (fold=each, dicodon set = 1, dicodon subset = each, method = N), we
can refer to this plot as the CI plot of R?uq for 1N.

And if you look at the CI plots at the end of this post for 2N, 3N,
1R, 2R, and 3R, you?ll see that:

a) the plot for 2N is almost as good as the plot for 1N (with just one
inversion of S and C slightly ?below the middle?;);

b) the plot for 3N is a jumble ? S?s and C?s are interspersed
throughout;

c) the plots for 1R,2R,3R are all also jumbles with interspersed S?s
and C?s.

So, these six plots alone tell us that we should expect our new set of
?two-ways? for Auq ITSELF to be better for dicodon sets 1 and 2 than
for 3. (By ?our new set of two-ways? I mean subset/method two-ways,
as we discussed previously, i.e. the two-ways that result from the
disappearance of u-Level (L,H)from the design.)

And in the next post I?m going to make following this one, you?ll see
that this prediction is borne out quite nicely. In particular, the
replacement of c on u with c on (u,u^2), together with the replacement
of u by u?=u/(1+u), sharpens the Bonferroni tables very nicely (so as
usual, kudos to your intuitions born of experience.) (Note also these
two-ways for Auq were done with the same custom t-tests we used for
the 3-ways, less the final mechanics for the 3-way from each pair of
two-ways; I mention this because of your cautionary note not to use
Excel for the tests.)

(II) Definition of slopes and their SE?s for the second new
regression.

For the second of the new regressions:

c on (e, u?, u?*e), u=1/(1+u)

would you take a moment to define the relevant slopes (or ?average
slopes?, as the case may be), and their associated SE?s? I?m anxious
to add these to the overall computation.

(III) CI plots of R?uq for 2N, 3N, 1R, 2R, and 3R.

(Again, if the following wrap, paste them into wide fixed font
document.)

2N:
-----m-----
c2,2,C
-------------------m------------------
b1,2,C
----m----
c1,2,C
----m---
a3,2,C
-----------m-----------
a1,2,C
-----------m----------
a3,2,S
------m-------
a1,2,S
---m--
b47,2,C
--m--
c1,2,S
---m----
b47,2,S
----m----
c2,2,S
----------m----------
b1,2,S

3N:
------------m-------------
a1,3,C
--------------m---------------
b1,3,S
-------m-------
c2,3,C
----m-----
b47,3,C
-------m--------
a3,3,S
----m----
c1,3,C
---------m---------
a1,3,S
--------m-------
c2,3,S
-----------------m-----------------
b1,3,C
-----m------
c1,3,S
-----------m------------
b47,3,S
---------m---------
a3,3,C

1R:
----------m---------
c2,1,S
----------------m----------------
b1,1,S
-------------m------------
a1,1,C
----------m----------
a1,1,S
-------m-------
c2,1,C
--------m--------
b47,1,C
---m---
c1,1,S
--------m-------
b47,1,S
----------------m---------------
a3,1,C
-------m------
c1,1,C
---------------------m---------------------
b1,1,C
-----------m-----------
a3,1,S

2R:
-------------m-------------
c2,2,S
-------m------
c2,2,C
-------------------m--------------------
b1,2,C
-------------------------------m------------------------------
b1,2,S
----------m---------
b47,2,S
------m-------
b47,2,C
-----m----
c1,2,C
----------m---------
a1,2,S
-----------m----------
a3,2,C
---------m---------
a1,2,C
------m------
c1,2,S
-----------m-----------
a3,2,S

3R:
------------------m------------------
b1,2,S
--------m--------
a1,2,C
-------m-------
a1,2,S
-----m----
b47,2,S
-----m-----
c1,2,C
------------m------------
a3,2,S
-------m------
b47,2,C
----------m----------
c2,2,C
---------------------m------------------
b1,2,C
----m---
c1,2,S
-------m------
c2,2,S
----------------m---
a3,2,C

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