R help - May 2008 - mixed effects models with nested factors

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)

 

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

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
	[[alternative HTML version deleted]]

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
>
> Luis Cayuela
> Departamento de Ecolog?a
> Universidad de Alcal?
> Crta. de Barcelona km. 33,600
> E-28871 Alcal? de Henares
> Madrid
> Espa?a
> Tlf: (+0034) 918856407
> Fax: (+0034) 918854929
>        [[alternative HTML version deleted]]
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

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 Ecolog?a
Universidad de Alcal?
Crta. de Barcelona km. 33,600
E-28871 Alcal? de Henares
Madrid
Espa?a
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