[R] GLM, LMER, GEE interpretation

From: Daniel Malter <daniel_at_umd.edu>
Date: Mon, 07 Jul 2008 03:48:53 -0400


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




-------------------------

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