# [R] Nested design and GLM: ....continue

Giovanni Bacaro bacaro at unisi.it
Thu May 25 22:33:33 CEST 2006

```Dear list members,
After your answeres to my firt mail I studied a lot (R-News n°5) and I
tried to perform my analysis:

First, to fit a GLM with a nested design I decided to use the function
"lmer" in package "lme4"
as suggested by Spencer Graves and Filippo Piro.
I remember you that my data were:

land use classes, 3 levels (fixed factor) = cla (R variable)
plot number, 98 levels each with 4 replicates (random factor within "cla")
= plotti (R variable)

number of species, totally 392 counts, response variable = sp (R variable)

Now, I startd my analysis as follow (after the creation of the data.frame
"bacaro"):

> summary(mod1) #sunto del modello

Generalized linear mixed model fit using PQL
Formula: sp ~ cla + (1 | cla:plotti)
Data: bacaro

AIC      BIC    logLik deviance
451.2908 467.1759 -221.6454 443.2908

Random effects:
Groups     Name        Variance Std.Dev.
cla:plotti (Intercept) 0.60496  0.77779
number of obs: 392, groups: cla:plotti, 98

Estimated scale (compare to 1)  0.6709309

Fixed effects:
Estimate Std. Error z value  Pr(>|z|)
(Intercept)  2.06406    0.14606 14.1316 < 2.2e-16 ***
cla2        -0.59173    0.17695 -3.3440 0.0008257 ***
cla3        -0.74230    0.83244 -0.8917 0.3725454
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
(Intr) cla2
cla2 -0.825
cla3 -0.175  0.145

> anova(mod1,test="Chsqr")
Analysis of Variance Table
Df Sum Sq Mean Sq
cla  2 11.352   5.676

Now, my questions are:
1) is the mod1 well specified? Have I said to R that "plotti" is my random
factor and that "plotti" is nested inside "cla" ("cla" as grouping
factor)? (can be  "lmer(sp~cla+(plotti|cla:plotti), data=bacaro,
family=poisson(link=log)" an alternative solution?)
2) Why if I try "lmer(sp~cla+(1|cla:plotti),..." or
"lmer(sp~cla+(1|plotti:cla),...." I obtain the same results?
3) why the anova summary don't say if differences in classes are
significance (or not significance)?

Thank you a lot for your help!
Giovanni

>I'd like to perform a glm analysis with a hierarchically nested design.
In particular,
>I have one fixed factor ("Land Use Classes") with three levels and a
random factor ("quadrat") nested within Land Use Classes with different
levels per classes (class artificial = 1 quadrat; class crops = 67
quadrats; and class seminatural = 30 quadrats).
>I have four replicates per each quadrats (response variable = species
richness per plot)

>Here some question about:
>1) could I analize these data using the class "artificial" (i.e. I have
only 1 level)?

>2) using R I'd like perfor a glm analysis considering my response
variable (count of species) with a Poisson distribution. How can I
develop my model considering the nested nature of my design? I'm sorry
but I don't know the right package to use.

>3) for the Anova analysis I'd like use a post-hoc comparison between
pairwise classes. What is the right procedure to do this? Is this
analysis performed in R?

--
Dr. Giovanni Bacaro
Università degli Studi di Siena
Dipartimento di Scienze Ambientali "G. Sarfatti"
Via P.A. Mattioli 4 53100 Siena
tel. 0577 235408
email: bacaro a unisi.it

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