Quant III, Homework 1 (the real deal)

Due Monday, 10/15

This is largely a redo of what you have done, but hopefully you now
understand.

I. Cross-national surveys with Huber et al. DV is the partyid dummy
variable. IV's are up to you, so long as you have enough. Please use
the logit link

a. Run the fully pooled logit. 

b. Run the fully same logit but with country dummies. How do the
   results differ from a). Loosely interpret the country dummies (that
   is, you do not need to go through a clarify exercise). 

c. Choose three countries and run a separate logit for each. How
   consistent are the results with a) AND b)

d. Take one variable and allow it to vary non-randomly by country (so
   interact, say, education with the country factor). This is done
   non-randomly.  Put in fixed country effects as before. What does
this logit tell you. Now we move to the previous variable.

e. Now interact whatever variable had a varying coefficient in d)
   (education) with a country level variable (perhaps number of
               parties). Do this in addition to what you did in
               d). How does this change the results of d).

Now we move to lmer. There are many ways to do this stuff, but the one
that I have checked (so a word to the wise!) is to ONLY load the
package arm, which then loads the parts of lme4 it needs. No
guarantees if you load lme4 directly.

f. Run the same model as in b) but with random effects (and random
   effects, fixed coefficients). How do the results of a), b) and f)
   differ?
(To answer this, you need to get estimates of the country random
   effects. You get this through ranef(lmer.object) and then
   se.ranef(lmer.object) where you have previously typed lmer.object<-lmer(stuff)

g. Now allow the same variable use used in d) (and e) to vary
   randomly. Using the functions mentioned in e), get the estimates of
   the random coefficients and se's. How do g) and d) differ?

h. Now repeat e), but with random variation of the coefficient. How do
   h) and e) differ?
    
II. I obviously care less about radon. Alex has provided an R
workspace with the Penn. data. Redo a) through h)
above. Some of these may be totally silly. If so, do and then show why
silly. What can you say about multilevel vs standard ols (with fixed
things) based on what you observe for I and II?

III. This can be turned in separately. This is prep for Winbugs.
Replicate the various Winbugs examples in 16.5. Try tweaking a bit to
make sure you are confident.