[R] GLM, LMER, GEE interpretation

[Daniel Malter]

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?

Thanks for any advice,
Daniel

Below is the output of the three models.

-----
GLM
-----

Call:
glm(formula = prob.bind ~ capacity * group, family = quasibinomial, 
    subset = c(combination == "gnl"))

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-18.9843   -4.1129    0.3816    6.0047   18.1858  

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 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

(Dispersion parameter for quasibinomial family taken to be 39.01488)

    Null deviance: 22672  on 359  degrees of freedom
Residual deviance: 15813  on 354  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

-----
LMER
-----
Generalized linear mixed model fit using Laplace 
Formula: prob.bind ~ capacity * group + (1 | subject) 
 Subset: c(combination == "gnl") 
 Family: quasibinomial(logit link)
   AIC   BIC logLik deviance
 11082 11109  -5534    11068
Random effects:
 Groups   Name        Variance Std.Dev.
 subject  (Intercept) 42.977   6.5557  
 Residual             26.845   5.1813  
number of obs: 360, groups: subject, 90

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

Correlation of Fixed Effects:
            (Intr) capcty group2 group3 cpct:2
capacity    -0.322                            
group2      -0.709  0.228                     
group3      -0.708  0.228  0.502              
capcty:grp2  0.235 -0.730 -0.310 -0.167       
capcty:grp3  0.233 -0.725 -0.166 -0.305  0.529      


-----
GEE
-----
 GEE:  GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
 gee S-function, version 4.13 modified 98/01/27 (1998) 

Model:
 Link:                      Logit 
 Variance to Mean Relation: Binomial 
 Correlation Structure:     Unstructured 

Call:
gee(formula = prob.bind ~ capacity * group, id = subject, 
    subset = c(combination == "gnl"), family = binomial, corstr =
"unstructured")

Summary of Residuals:
       Min         1Q     Median         3Q        Max 
-0.8397112 29.7353417 59.2605133 89.2223581 99.8099842 


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

Estimated Scale Parameter:  39.28916
Number of Iterations:  3

Working Correlation
            [,1]      [,2]       [,3]        [,4]
[1,]  1.00000000 0.1632065 0.04525213 -0.08946253
[2,]  0.16320653 1.0000000 0.17635584  0.16703313
[3,]  0.04525213 0.1763558 1.00000000  0.22291895
[4,] -0.08946253 0.1670331 0.22291895  1.00000000



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