[R] Linear mixed effects model ?

[Daniel Perkins]

I am looking for some advice on an appropriate statistical analysis in R

*Experimental question* : We are interested in how communities from 
different streams may vary in their response to experimental 
temperature. Specifically we are interested to test for differences in 
the slope and intercept of the relationship between temperature and 
oxygen consumption between the different stream communities.

*Outline of experiment*

There were four streams and from each we took samples which had a 
characteristic community of organisms. These four different communities 
are labelled “S1,.. S4.

Each ‘Stream’ was incubated together in the same water bath at six 
temperatures in succession, giving covariates (~ 5,10,15,20,25,and 30°C) 
to the factor “Temp”.

However this also meant six repeated measures were made on the same 
‘Stream’ over time. As time between incubations varied ‘Time’ is given a 
categorical label a,....f.

This procedure was repeated four times using different samples from the 
same streams, thus giving ‘Replicates’ labelled 1,...4. Each ‘Replicate’ 
had different temperature values but always six values in total.

The response variable measured in all 96 incubations, was the rate at 
which the communities consumed oxygen over a given time in incubation: 
‘Rate’

Some incubation’s were excluded (5 from 96)

*Models*

Ideally we would do an ANCOVA to test for differences in slope or 
intercepts for the different streams. However as there were repeated 
measures and unequal n and unbalanced design, I have used a linear mixed 
effect model (from nlme package in R) in the form:

model <- lme (Rate ~ Temp* Stream, random = ~ Time|Replicate)

*Question* : Do these models appropriately account for the temporal / 
spatial pseudoreplication in the experimental design ?

Many thanks in advance

Daniel