lmer vs glmmPQL

Hi All,

I'm doing a simple logistic regression with one fixed and one random  
effects, and I'm comparing the results I got from lmer() and  
glmmPQL(). I'm finding that lmer gives my a "better" p-value for my  
fixed effects. Because I'm a paranoid old man I'd go for the glmmPQL  
results then, but my collaborators are less paranoid and I'm sure  
they'd prefer the results from lmer. Am I too conservative? (I  
ralise it looks like I'm asking for counselling more than advice,  
but there you go...).

Best,

Federico

My models:

mod1 = glmmPQL(y ~ genotype, random = ~1|block, family = binomial,  
data)
mod2 = lmer(y ~ genotype + (1|block), family = binomial, data)

my data:

data

 genotype block y.1 y.2
1  A     a  16  29
2     B     a  19  26
3      C     a  23  23
4  A     c   6  24
5     B     c  11  11
6      C     c  13  14
7  A     b   4  17
8     B     b  10   8
9      C     b  12   6

data[[1]]

[1] A B    C     A B    C     A B    C
attr(,"contrasts")
       [,1] [,2]
B       1   -1
A   -2    0
C        1    1
Levels: B A C

my results:

summary(mod1)

Linear mixed-effects model fit by maximum likelihood
Data: dat
 AIC BIC logLik
  NA  NA     NA

Random effects:
Formula: ~1 | block
        (Intercept)  Residual
StdDev: 1.285532e-06 0.8077838

Variance function:
Structure: fixed weights
Formula: ~invwt
Fixed effects: y ~ genotype
                Value  Std.Error DF   t-value p-value
(Intercept) -0.3327269 0.12516679  4 -2.658269  0.0565
genotype1    0.3288359 0.09065856  4  3.627190  0.0222
genotype2    0.1138920 0.14947659  4  0.761938  0.4885
Correlation:
         (Intr) gntyp1
genotype1 -0.068
genotype2 -0.027 -0.019

Standardized Within-Group Residuals:
      Min         Q1        Med         Q3        Max
-1.0807836 -0.8047002 -0.4620287  0.8940787  1.5832300

Number of Observations: 9
Number of Groups: 3

summary(mod2)

Generalized linear mixed model fit by the Laplace approximation
Formula: y ~ genotype + (1 | block)
  Data: dat
  AIC   BIC logLik deviance
13.92 14.71 -2.960    5.919
Random effects:
Groups Name        Variance Std.Dev.
block  (Intercept)  0        0
Number of obs: 9, groups: block, 3

Fixed effects:
           Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.33273    0.12652  -2.630 0.008541 **
genotype1    0.32884    0.09164   3.588 0.000333 ***
genotype2    0.11389    0.15109   0.754 0.450965
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Correlation of Fixed Effects:
         (Intr) gntyp1
genotype1 -0.068
genotype2 -0.027 -0.019




--
Federico C. F. Calboli
Department of Epidemiology and Public Health
Imperial College, St. Mary's Campus
Norfolk Place, London W2 1PG

Tel +44 (0)20 75941602   Fax +44 (0)20 75943193

f.calboli [.a.t] imperial.ac.uk
f.calboli [.a.t] gmail.com