[R-sig-ME] lmer vs glmmPQL

[Ken Beath]

On 24/06/2009, at 2:18 AM, Federico Calboli wrote:

> 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...).
>

This seems to results from the use of a t-test with few df in glmmPQL  
and z in lmer. z seems fine to me. What is more of a problem is that  
your random effects variance is effectively 0. There are only 3 blocks  
so fitting a random effects model will be difficult and appears  
unnecessary.

Ken




> 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
>
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