[R] GLM, LMER, GEE interpretation

[Ben Bolker]

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

> 
> Hi, my dependent variable is a proportion ("prob.bind"), and the independent
> variables are factors for group membership ("group") and a covariate
> ("capacity"). I am interested in the effects of group, capacity, and their
> interaction. Each subject is observed on all (4) levels of capacity (I use
> capacity as a covariate because the effect of this variable is normatively
> linear). I fit three models, but I am observing differences between the
> three.
> 
> The first model is a quasibinomial without any subject effects using glm.
> The second is a random-effects model using lmer. The third model is a
> generalized estimating equation using gee from the gee package in which I
> cluster for the subject using an unstructured correlation matrix. The
> results of the first and the third model almost coincide, but the second,
> using lmer, shows an insginficant coefficient where I would expect a
> significant one. The other 2 models show the coefficient significant. I do
> not really have experience with gee. Therefore I apologize in advance for my
> ignorant question whether one of lmer and gee is preferable over the other
> in this setting?

[glm] 
Coefficients:
>                 Estimate Std. Error t value Pr(>|t|)    
> (Intercept)      -3.4274     0.4641  -7.386 1.10e-12 ***
> capacity          0.9931     0.1281   7.754 9.55e-14 ***
> group2            0.7242     0.6337   1.143  0.25392    
> group3            2.0264     0.6168   3.286  0.00112 ** 
> capacity:group2  -0.1523     0.1764  -0.863  0.38864    
> capacity:group3  -0.3885     0.1742  -2.231  0.02633 *  

[lmer]
> Generalized linear mixed model fit using Laplace 
> Formula: prob.bind ~ capacity * group + (1 | subject) 
>  Subset: c(combination == "gnl") 
>  Family: quasibinomial(logit link)
 [snip]
> Fixed effects:
>                 Estimate Std. Error t value
> (Intercept)      -3.8628     1.2701  -3.041
> capacity          1.1219     0.1176   9.542
> group2            0.9086     1.7905   0.507
> group3            2.3700     1.7936   1.321
> capacity:group2  -0.1745     0.1610  -1.083
> capacity:group3  -0.3807     0.1622  -2.348

[gee]
> Coefficients:
>                   Estimate Naive S.E.    Naive z Robust S.E.   Robust z
> (Intercept)     -3.4798395  0.4910274 -7.0868545   0.4739913 -7.3415687
> capacity         1.0149659  0.1366365  7.4282170   0.1284162  7.9037210
> group2           0.7781014  0.6691731  1.1627806   0.7424769  1.0479807
> group3           2.0720270  0.6527565  3.1742727   0.6234005  3.3237495
> capacity:group2 -0.1750448  0.1877361 -0.9323982   0.2060484 -0.8495325
> capacity:group3 -0.4021872  0.1865916 -2.1554413   0.1724780 -2.3318168
> 

  I assume you're talking about the differences in
the estimated standard errors of the group3 (and group2)
parameters (everything else looks pretty similar)?

  All else being equal I would trust lmer slightly more
than gee (and the non-clustered glm is not reliable for
inference in this situation, since it ignores the clustering) --
but I'm pretty ignorant of gee, so take that with a grain of salt.
I would make the following suggestions --

1. consider whether it even makes sense to test the
significance of the group3 main effect in the presence
of the capacity:group3 interaction.  Is the value capacity=0
somehow intrinsically interesting?

2. all of these standard error estimates are pretty crude/
rely on large-sample assumptions (how big is your data set?);
unfortunately more sophisticated estimates of uncertainty
are currently unavailable for GLMMs in lmer.  I would try
your problem again with glmmML, just to check that it gives
similar answers to lmer.

3. if you need more advice, consider asking this on r-sig-mixed
instead ...

  Ben Bolker