FW: [R] glmmPQL and random factors

[Lorenz.Gygax@fat.admin.ch]

I have just realised that I sent this to Per only. For those interested on
the list:

-----Original Message-----
From: Gygax Lorenz FAT 
Sent: Tuesday, September 14, 2004 4:35 PM
To: 'Per Toräng'
Subject: RE: [R] glmmPQL and random factors

Hi Per,

> glmmPQL(Fruit.set~Treat1*Treat2+offset(log10(No.flowers)), 
> random=~1|Plot, family=poisson, data=...)
> 
> Plot is supposed to be nested in (Treat1*Treat2).
> Is this analysis suitable?

As far as I understand the methods and with my experience using such
analyses, I would say that the model is ok the way you specified it.

glmmPQL (and the underlying lme) is so intelligent (a thousand thanks to the
developpers!) as to recognise if the treatments are fixed per plot, i.e.
only one level of the two treatments appears in each plot. The denominator
degrees of freedom in the anova table are adjusted automatically. I.e. your
denominator df should  be the number of plots minus five, the number of dfs
you need for the fixed effects (Treat1, Treat2, the interaction, the
covariate and the one df you always loose from the total of observations).

> Moreover, what is the meaning of typing 
> random=~1|Plot compared to random=~Treat1*Treat2|Plot?

The first version means, that the intercept / overall mean can vary from
plot to plot. I.e. each plot may have another mean due to the fact that it
grows somewhere else in addition to the differing treatments.

The second version tries to model a difference in reaction to treatment 1
and 2 for each of the plots (which does not make sense in your case as each
plot is only subjected to one kind of treatment).

In a crossed design, i.e. if you could have treated your plants individually
and had all treatment combinations in each of the plots, the first version
implies that all the plots react in the same consistent way to the
treatments. I.e. that the general level of each plot may be different, but
the differences due to treatment are the same in each plot, the reaction of
the plots are shifted but have the same shape (this is the same as saying
that you only consider main effects of treatment and plot).

The second version allows to estimate the reactions for each plot, i.e. in
addition to a general shift, the treatments may have (slightly) different
effects in each plot. This is the same as saying that you consider
interactions between your fixed and random effects. See also the terrific
book by Pinheiro & Bates (Mixed Effects Modelling in S and S-Plus, Springer,
2000).

Cheers, Lorenz
- 
Lorenz Gygax
Tel: +41 (0)52 368 33 84 / lorenz.gygax at fat.admin.ch      
Centre for proper housing of ruminants and pigs
Swiss Federal Veterinary Office