R help - Oct 2009 - interpreting glmer results

Hi all,

I am trying to run a glm with mixed effects. My response variable is
number of seedlings emerging; my fixed effects are the tree species
and distance from the tree (in two classes - near and far).; my random
effect is the individual tree itself (here called Plot). The command
I've used is:

mod <- glmer(number ~ Species + distance + offset(area) + (1|Plot),
family = poisson)


There is an area offset because the plot in which seedlings were
counted was a wedge with its point at the tree base, and therefore the
area of the part of plot far from the tree was greater than the area
of the plot closer to the tree.

The results I'm getting are:

Generalized linear mixed model fit by the Laplace approximation
Formula: number ~ Species + distance + offset(area) + (1 | Plot)
   AIC   BIC logLik deviance
 145.6 168.7 -64.82    129.6
Random effects:
 Groups Name        Variance Std.Dev.
 Plot   (Intercept) 0.60205  0.77592
Number of obs: 132, groups: Plot, 132

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)
(Intercept) -138.8423     0.4704  -295.1  < 2e-16 ***
SpeciesCr     -0.9977     0.6259    -1.6  0.11091
SpeciesDb     -1.2140     0.6945    -1.7  0.08046 .
SpeciesHk     -2.0864     1.2134    -1.7  0.08553 .
SpeciesPa     -2.6245     1.2063    -2.2  0.02958 *
SpeciesPs      1.3056     0.4027     3.2  0.00119 **
distancen    121.7170     0.3609   337.3  < 2e-16 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Correlation of Fixed Effects:
          (Intr) SpcsCr SpcsDb SpcsHk SpecsP SpcsPs
SpeciesCr -0.423
SpeciesDb -0.391  0.295
SpeciesHk -0.223  0.169  0.152
SpeciesPa -0.222  0.170  0.153  0.088
SpeciesPs -0.732  0.507  0.458  0.262  0.263
distancen -0.648 -0.020 -0.002 -0.003 -0.006  0.085

Here, clearly, distance from the tree has an effect, but I want to
know whether the identity of the species influences seedling numbers
in general. I am unable, however, to make much sense of the output.
Also, what does correlation of fixed effects really tell me?

Many thanks for any help.

Cheers,
Umesh Srinivasan,
Bangalore, India

On Mon, Oct 5, 2009 at 8:52 AM, Umesh Srinivasan
<umesh.srinivasan at gmail.com> wrote:
> Hi all,
[snip]
>
> Fixed effects:
> ? ? ? ? ? ? Estimate Std. Error z value Pr(>|z|)
> (Intercept) -138.8423 ? ? 0.4704 ?-295.1 ?< 2e-16 ***
> SpeciesCr ? ? -0.9977 ? ? 0.6259 ? ?-1.6 ?0.11091
> SpeciesDb ? ? -1.2140 ? ? 0.6945 ? ?-1.7 ?0.08046 .
> SpeciesHk ? ? -2.0864 ? ? 1.2134 ? ?-1.7 ?0.08553 .
> SpeciesPa ? ? -2.6245 ? ? 1.2063 ? ?-2.2 ?0.02958 *
> SpeciesPs ? ? ?1.3056 ? ? 0.4027 ? ? 3.2 ?0.00119 **
> distancen ? ?121.7170 ? ? 0.3609 ? 337.3 ?< 2e-16 ***
> ---
> Signif. codes: ?0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Correlation of Fixed Effects:
> ? ? ? ? ?(Intr) SpcsCr SpcsDb SpcsHk SpecsP SpcsPs
> SpeciesCr -0.423
> SpeciesDb -0.391 ?0.295
> SpeciesHk -0.223 ?0.169 ?0.152
> SpeciesPa -0.222 ?0.170 ?0.153 ?0.088
> SpeciesPs -0.732 ?0.507 ?0.458 ?0.262 ?0.263
> distancen -0.648 -0.020 -0.002 -0.003 -0.006 ?0.085
>
> Here, clearly, distance from the tree has an effect, but I want to
> know whether the identity of the species influences seedling numbers
> in general. I am unable, however, to make much sense of the output.

As with other linear model type functions in R the summary method
returns tests based on a factor's contrasts (treatment by default,
comparing other levels to a baseline level).  To get an omnibus test
of a factor, one option is to create a model with and without the
factor and perform an LRT:

library(lme4)
example(glmer)
gm0 <- glmer(cbind(incidence, size - incidence) ~ 1 + (1 | herd),
family = binomial, data = cbpp)
anova(gm0, gm1)
> Also, what does correlation of fixed effects really tell me?
>
These can be of interest for inference (e.g. a confidence region for
two of the coefficients is an ellipse with eccentricity defined by
their correlation).


hth,

Kingsford


> Many thanks for any help.
>
> Cheers,
> Umesh Srinivasan,
> Bangalore, India
>
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