[R] GLM, LMER, GEE interpretation

[Ben Bolker]

Daniel Malter <daniel <at> umd.edu> writes:

> 
> Thanks for your answers. I appreciate your help. I tried the glmmML.
> However, it seems glmmML does not allow for a quasibinomial fit as I did
> with the models I used. I have large overdispersion which I account for
> using a quasibinomial with scaling parameter. Further, I have 360
> observations  - is that considered large enough for asymptotics?
> 
> The capacity covariate ranges from 2 to 5 in steps of 1. I repeated the
> analysis subtracting 2 (because then the "0" capacity makes more sense and
> is of intrinsic interest) and get the "same" results. The group and
> group*capacity interaction make sense as I want to investigate a level and a
> slope difference for the groups. However, I am worried about the correlation
> of fixed effects. LMER gives me the following correlation matrix for the
> fixed effects: 
> 
>             (Intr) I(c-2) group2 group3 I(-2):2
> I(capcty-2) -0.143                             
> group2      -0.707  0.101                      
> group3      -0.705  0.101  0.499               
> I(c-2):grp2  0.104 -0.730 -0.135 -0.074        
> I(c-2):grp3  0.104 -0.725 -0.073 -0.129  0.529 
> 
> I will try to leave out the capacity effect altogether and just model a
> group and a group slope effect. Does that make sense?
> 
> Thanks,
> Daniel

  Some quick (incomplete) answers (hoping for someone else to 
jump in):

1. overdispersion of 39 is very high, often indicates some nasty
lack of fit -- have you looked at graphical summaries etc. to see
that it's "just" high variance?  Alternatively, this could just
be telling you about the fact of clustering, and it's possible
that your subject-specific random effect is taking care of the
overdispersion.  I don't know how to extract an estimate of
the scale parameter from a (g)lmer fit though ...  are you fitting
quasibinomial, or binomial, in the GEE case?  (One quick way to
see if the scale parameter is big is to see if anything changes much
if you run the (g)lmer model with binomial rather than QB.)

2. those correlations among parameters don't look *terribly*
high to me -- I would worry about abs(c) > 0.8 ....

3. 360 observations (and 90 clusters) does seem pretty reasonable
for 6 fixed parameters + 1 random effect ...

4. I wouldn't be 100% certain that glmer is handling QB right --
have you tried a simulation with known overdispersion parameters?

5. I'm surprised you can shift the origin on capacity and
get the "same" results, although maybe you just mean significant
one way/insignificant the other ...  If it makes sense to compare
groups at capacity=2, then testing the significance in this case
seems OK, even in the presence of the group:capacity interaction.
(Although consider what you would say if the answer changed if
you modeled (capacity-5) rather than (capacity-2))

6. I don't understand what a "group slope effect" is ... ?