Plan for Friday, Oct. 25 (3 PM meeting)

I think a reasonable plan would be to first tie up loose ends in what we
had planned to cover this past Friday, and then discuss more in Ch. 4 of
Harrell, to the end of p. 72.  (If we finish to p. 72, we may be able to
finish Ch. 4 the next week, even though we will only have 90 minutes for
the Nov. 1 meeting.)  Specifically, the loose ends are:

               Sec. 3.8   D.G.
 
                  p. 59   J.S.
   
        rest of Sec 4.3   A.K.  (Can you find a small economic or 
                                 medical data set that has an estimated
                                 coefficient with the "wrong sign"?)
 
               Sec. 4.4   C.P. 
 
For the new material, I think it may be best not to have specific section
assignments.  Rather, we'll just have a general group discussion about pp. 
62-72 (& the very last part of p. 61), with the discussion concentrating
on parts that group members have questions about.  (We'll consider the
material (sub)section by (sub)section, but move right along if no one has
any questions.)

My guess is that some portions of the material will be familiar to most,
and will warrant litle discussion.  Other parts may be generally more
confusing, and will warrant more discussion, but it isn't clear who can
best explain the trouble spots, and so I won't suggest specific
assignments.

Below, I'll indicate some portions of the material that may warrant some
discussion (but in some cases it may be that we won't figure out for sure
at this point what Harrell means, and we'll have to move ahead and hope
that matters are clarified later in the book).

(a) Is the shrinkage factor on the last line (not counting footnote) of
p. 63 a special case of (4.1) on p. 63?  Perhaps we can consider both
formulas for the case of 
  y = beta_0  +  beta_1 * x_1  +  beta_2 * x_2  +  beta_3 * (x_2)^2  +  e.
(It seems to me that if we generate data according to such a model, we can
(try to) compute the shrinkage factor(s), and also compute the shrunken 
estimate of beta given by (4.3) on p. 64 ... and see if the shrunken
estimates are closer to the truth.  *** Let's all try this using 
  beta_0 = 0,
  beta_1 = 1,
  beta_2 = 1,
& beta_3 = 1,
with iid N(0, 1) error terms, (each person) choosing a sample size and
design (x values) to make an "interesting" example. ***  With regard to
the shrinkage factors, the 2nd one should be easy (just use (4.2)), but
for the 1st one you'll have to figure out what is meant by the model
chi-square (it's a likelihood ratio statistic, but you need to figure out
how to compute it's value).)

(b) Can you explain why the 1st sentence of Sec. 4.6 is true?

(c) In the last sentence of the 2nd to last paragraph on p. 65, does
Harrell mean that VIF is *never* very informative?  Also, what exactly
does he mean by variables being algebraically connected connected to each
other?

(d) Can we try out the MGV method using a simple example like the 2
variable one given near the top of p. 68?  Then do we dare try it with 3
variables?

(e) Can anyone explain the part of subsection 4.7.4 on p. 70 after the
frist 2 sentences?  (I.e., explain the part that begins with "For the
ordinal count" and ends with "new summary vatiable.")

(f) Can anyone explain the last paragraph of subsection 4.7.5 on p. 72?

Looking ahead, the next 2 chapters after Ch. 4 are relatively short
compared to Ch. 4.  But before we start Ch. 5, it may be good to spend at
least a week trying some problems from the book or trying some of the
techniques described on some examples of our own.  (Oddly, Ch. 4 doesn't
have any end of the chapter problems.  Still, I think we should work
through a few things from Ch. 4 before moving on to Ch. 5.)

CDS