[R] GLM, LMER, GEE interpretation

Mon Jul 7 23:24:13 CEST 2008

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

-------------------------
cuncta stricte discussurus
-------------------------

-----Ursprüngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von Ben Bolker
Gesendet: Monday, July 07, 2008 1:41 PM
An: r-help at stat.math.ethz.ch
Betreff: Re: [R] GLM, LMER, GEE interpretation

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

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.