[R] mixed effects models with nested factors

[Luis Cayuela]

Thanks for the help provided to fit the model. I still have two questions:

1) What is the syntax for nested fixed and random factors. I have tried 
using the %in% operator but it does not work. The model I want to fit would 
be as follow:

lmer 1 <- lmer(Growing ~ Seed + Species%in%Seed + Treatment + 
(1|Block%in%Treatment), data)

2) Seed, Species and Treatment are intra-subject factors. This means that an 
ANOVA of repeated measure should apply here. How should this be specified in 
the model? Or should I assume that this is incorporated by specifying the 
Block as a random factor?

All the best,

Luis

Luis Cayuela
Departamento de Ecología
Universidad de Alcalá
Crta. de Barcelona km. 33,600
E-28871 Alcalá de Henares
Madrid
España
Tlf: (+0034) 918856407
Fax: (+0034) 918854929
----- Original Message ----- 
From: "Douglas Bates" <bates at stat.wisc.edu>
To: "Luis Cayuela" <luis.cayuela at uah.es>
Cc: <r-help at r-project.org>
Sent: Thursday, May 15, 2008 5:22 PM
Subject: Re: [R] mixed effects models with nested factors


On Thu, May 15, 2008 at 9:22 AM, Luis Cayuela <luis.cayuela at uah.es> wrote:
> Hi everybody,

> I am trying to fit a model with the lmer function for mixed effects. I 
> have an experimental design consisting of 5 field plots. Each plot is 
> divided in 12 subplots where the influence of three factors on the growing 
> of tree seedlings is tested: (1) seed (1 = presence; 0 = absence); (2) 
> seedling species (oak holm vs. pine); (3) treatment (three different 
> treatments). In each of these subplots we planted 13 seedlings. Therefore 
> I would have a model with three fixed factors and one random factor (a 
> block?). If I´m not wrong the model would be as follows:

> model2 <- lmer(Growing ~ Seed + Species + Treatment +(Seed + Species + 
> Treatment|Block), data)

That's unlikely. This specification would fit 5 fixed effects
parameters and 5, possibly correlated, random effects for each level
of the Block factor.  This would require estimating a total of 15
variance-covariance parameters for the random effects from the 5
blocks.

Can you indicate how many random effects you expect to obtain and how
many variance-covariance parameters would be involved?  For example, a
model with a simple random effect would be expressed as

 lmer(Growing ~ Seed + Species + Treatment + (1|Block), data)

and would involve estimating the 5 fixed effects and one variance for
the random effects.
> My first question is: if the three fixed factors occur within-subjects 
> (considering the plot as a subject), is the model correctly defined 
> (assuming no interactions)? Should I specify the model in some other way?
>
>
>
> I second problem I had is that the factors are not crossed because some of 
> the seedling died during the experiment. This means that some factors are 
> nested. Specifically Species is nested within Seed and Block would be 
> nested within Treatment. I have tried to use the %in% specification for 
> nested designs but it does not work.
>
>
>
> model2 <- lmer(Growing ~ Seed + Species%in%Seed + Treatment +(Seed + 
> Species + Treatment|Block%in%Treatment), data)
>
>
>
> I get the following error:
>
>
>
> Error en lmer(Growing ~ Seed + Species %in% Seed + Treatment +  : ..
>
>  Leading minor of order 5 in downdated X'X is not positive definite
>
>
>
> I would appreciate some help to fit this model.
>
>
> Thanks to everybody,
>
> Luis