Dear list members,

I am trying to model in R an experiment with the BACI structure, that is, consisting in a Before-After factor and a Control-Impacted one, both fixed. I had the same sampling structure in four locations, what makes location a random blocking factor. That would be relatively easy for me if I had not also some samplings Before (2 samplings) and After (3 samplings) the affection we generated in our systems.

In short, I have a random blocking factor, two fixed factors (BA and CI) and a random sampling factor nested within BA (BA/sampling). The number of samples within each cell is ten and I have not empty cells. The sources of variation I am interested in the model are:

-BA
-CI
-BA*CI
-BA/sampling
-CI*(BA/sampling)

I have tried many different types of syntaxes and none gives me a valid result. The packages I have used are nlme and lme4, with some preference to the first as p values are obtained more easily. One of the syntaxes I have used:

model<-lme(Response~BA*CI+BA/Sampling+CI*BA/Sampling,random=~1|Block),

gives the following error:

Error in MEEM(object, conLin, control$niterEM) : 
  Singularity in backsolve at level 0, block 1

Below I send an example of a dataset similar to what I am using (with just two cases per cell and three blocks for brevity).

Block	BA		CI		sampling	Response
a		B		C		1			
a		B		C		1			
a		B		C		2
a		B		C		2
a		A		C		3
a		A		C		3
a		A		C		4
a		A		C		4
a		A		C		5
a		A		C		5
a		B		I		1			
a		B		I		1			
a		B		I		2
a		B		I		2
a		A		I		3
a		A		I		3
a		A		I		4
a		A		I		4
a		A		I		5
a		A		I		5
b		B		C		1			
b		B		C		1			
b		B		C		2
b		B		C		2
b		A		C		3
b		A		C		3
b		A		C		4
b		A		C		4
b		A		C		5
b		A		C		5
b		B		I		1			
b		B		I		1			
b		B		I		2
b		B		I		2
b		A		I		3
b		A		I		3
b		A		I		4
b		A		I		4
b		A		I		5
b		A		I		5
c		B		C		1			
c		B		C		1			
c		B		C		2
c		B		C		2
c		A		C		3
c		A		C		3
c		A		C		4
c		A		C		4
c		A		C		5
c		A		C		5
c		B		I		1			
c		B		I		1			
c		B		I		2
c		B		I		2
c		A		I		3
c		A		I		3
c		A		I		4
c		A		I		4
c		A		I		5
c		A		I		5

I would be eternally grateful to the list if someone can lead me to the answer of the matter.

All the best,

Aitor Larraņaga


Dr. Aitor Larraņaga
Laboratory of Stream Ecology
Dept. of Plant Biology and Ecology
Fac. of Science and Technology
University of the Basque Country
PO Box 644
48080 Bilbao
Spain

phone: +34 94 601 5939
email: aitor.larranagaa@ehu.es
fax: +34 94 601 3500
http://www.ehu.es/streamecology/ 


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