Difficulties in trying to do a mixed effects model using the lmer function

Dear people of the help list

I am drying to analyze my data using the 'lmer' function and I keep having problems.

This is the model:

fm1<-lmer(dbh~spec+scheme+(1|Plot),data=d, REML=FALSE).

I analyse tree size (dbh) of  3 different species (spec) and  3 planting schemes (scheme). I have 5 plots, which I hope to model as a random factor. (However, the subsequent output is based on some simplified dummy data, which is based on only two plots and ha only few observations).

No I do:

anova(fm1)

and I get some output, which I don't understand. Looks like this:

Analysis of Variance Table
       Df Sum Sq Mean Sq F value
spec    2 6.098 3.0490  0.6142
scheme  2 13.161  6.5803  1.3255

The problems I have are:
(1) How can I get the P-values?
(2) How can I get the overall model statistic?

Than I do:

summary(fm1)

and get:
Linear mixed model fit by maximum likelihood
Formula: dbh ~ spec + scheme + (1 | Plot)
   Data: d
   AIC BIC logLik deviance REMLdev
 147.2 157  -66.6    133.2   125.8
Random effects:
 Groups   Name        Variance Std.Dev.
 Plot     (Intercept) 0.0000   0.0000
 Residual             4.9644   2.2281
Number of obs: 30, groups: Plot, 2

Fixed effects:
            Estimate Std. Error t value
(Intercept)   6.9074     0.9424   7.329
specCED       0.3859     1.0265   0.376
specTAB       0.8585     0.9828   0.874
schemeMON     0.6572     0.9554   0.688
schemePRO    -1.0344     1.1259  -0.919

Correlation of Fixed Effects:
          (Intr) spcCED spcTAB schMON
specCED   -0.537
specTAB   -0.529  0.500
schemeMON -0.588  0.002 -0.072
schemePRO -0.565  0.064  0.063  0.510

What is this? What does it tell me?

The statistics help advised me to do a second model, like this:

fm2<-lmer(dbh~scheme+(1|Plot),data=d,REML=FALSE)
anova(fm1,fm2)

But why would I compare the two models?

 What I get is:
Data: d
Models:
fm2: dbh ~ scheme + (1 | Plot)
fm1: dbh ~ spec + scheme + (1 | Plot)
    Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
fm2  5 143.96 150.97 -66.982
fm1  7 147.21 157.01 -66.602 0.7584      2     0.6844

What does this mean? Why Chi?

Finally I would like to do some LSD post hoc tests, but I have no idea how to do it.

In the end I would like to be able to report something like: 'DBH differed significantly between, species, planting schemes, and plots (Fx,xx = X; P = X). DBH of species 1 was significantly larger than DBH of species 2 (LSD post hoc test, P = X)'.

I greatly appreciate any suggestions! Thank You a lot for Your help!

Kind regards,

Judith

PS. the complete output is attached.



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Judith Riedel
ETH Zurich
Institute of Agricultural Sciences
Applied Entomology
Schmelzbergstrasse 9/LFO
8092 Zurich
Switzerland

Tel:  ++41 44 632 3923
Fax: ++41 44 632 1171
judith.riedel at ipw.agrl.ethz.ch<mailto:judith.riedel at ipw.agrl.ethz.ch>
http://www.em.ipw.agrl.ethz.ch