R help - Jan 2008 - Random and fixed effect model with a covariate

Dear All,

I wonder if anyone can please offer any advice on a model including 2 fixed
effects and 1 random effect, as well as a covariate?

The experimental design is as follows:
I have a two by two factor design, where the two factors, Age (A) and Group size
(G), both have 2 levels (old or young, and 1 or 3 respectively), and I am
interested in the effect of these factors upon a continuous Response variable
(R).

The data is from social insects, so the above design is repeated for several
colonies. I think that Colony (C) should be a random factor, as they were taken
from a larger pool of available colonies. Identification number (I) is different
for each individual.

Furthermore, I have a covariate, Mass (M), which could have an effect upon R.

Do you know which of the below (if any) would be the most appropriate model
please?

model<-lme(R~A*G*M,random=~1|C/I)
model<-lme(R~A*G+M,random=~1|C/I)

or is it necessary to state that A and G are factors as below:

model<-lme(R~as.factor(A)*as.factor(G)*M,random= ~1|C/I)
model<-lme(R~as.factor(A)*as.factor(G)+M,random= ~1|C/I)

Do you also please have any advice upon the effect it would have to change the
order in which the factors and covariate are placed in the model? When I tried
moving them around in the above models it changed the test statistics slightly.

Many thanks in advance for any help you can give, it?s very much appreciated.

Sophie Armitage

Dear Sophie,
> I wonder if anyone can please offer any advice on a model 
> including 2 fixed effects and 1 random effect, as well as a 
> covariate? 
> 
> The experimental design is as follows:
> I have a two by two factor design, where the two factors, Age 
> (A) and Group size (G), both have 2 levels (old or young, and 
> 1 or 3 respectively), and I am interested in the effect of 
> these factors upon a continuous Response variable (R).
> 
> The data is from social insects, so the above design is 
> repeated for several colonies. I think that Colony (C) should 
> be a random factor, as they were taken from a larger pool of 
> available colonies. Identification number (I) is different 
> for each individual.
> 
> Furthermore, I have a covariate, Mass (M), which could have 
> an effect upon R.
This sounds all quite reasonable.
> Do you know which of the below (if any) would be the most 
> appropriate model please?
> 
> model<-lme(R~A*G*M,random=~1|C/I)
> model<-lme(R~A*G+M,random=~1|C/I)
Well, this depends on your research question and whether or not interactions
between A:M, A:G and A:G:M can be interpreted meaningfully, I would say.
> or is it necessary to state that A and G are factors as below:
> 
> model<-lme(R~as.factor(A)*as.factor(G)*M,random= ~1|C/I)
> model<-lme(R~as.factor(A)*as.factor(G)+M,random= ~1|C/I)
Yes, indeed, you need to specify factors as such. If they are factors it
possibly makes sense to change their type in the data frame as many other
functions (e.g. plotting functions) do different things with factors rather than
continuous variables.

If your factor levels include letters then R automatically turns these variables
into factors while you read the data. A two-level factor can be coded
numerically with 0 and 1s instead of explicitly turning it into a factor
variable.
> Do you also please have any advice upon the effect it would 
> have to change the order in which the factors and covariate 
> are placed in the model? When I tried moving them around in 
> the above models it changed the test statistics slightly. 
Well, the standard anova output follows a type I sum-of-squares logic, i.e. each
addditional variable (lower down in the list) is tested for a significant
improvement of the model so far. Thus, the seuquence has some importance.

If you use anova (..., type= 'marginal') you can follow a type III
sum-of-squares logic, i.e. it is tested whether dropping a specific variable
from the full model leads to a significant deterioration of the model or not.

In my perception, there are different schools of thought that either prefer the
one or the other. Thus, perhaps you should use what is commonly used in your
field.

Regards, Lorenz
- 
Lorenz Gygax, Dr. sc. nat., postdoc
Federal Veterinary Office
Centre for proper housing of ruminants and pigs
Agroscope Reckenholz-T?nikon Research Station ART
T?nikon, CH-8356 Ettenhausen / Switzerland