Spencer,

Thank you for the kind and elaborate reply to my previous post.

I did consider the option you suggested and many variations. Depending on the order of the random factors, lme will either give the same output as the aov model for soiltype or for habitat, but not both in the same model. 

The closest I came was 

          anova(lme(NA.1~soiltype*habitat,random=~1|destination/soiltype))

However, it apppears that in this case the interaction is tested at the same level as soiltype.

In this post, a small sample dataset with a brief explanation of the meaning of the different column titles is included below. Also, I included both the aov model and the lme model.

Hopefully, this will help to get closer to a solution to my problem.

Best regards,

René Eschen.

___

#Small sample dataset
#
data=read.table("Sample dataset.csv",header=T) 
require(nlme)
soiltype=factor(soiltype)
habitat=factor(habitat)
destination=factor(destination)
origin=factor(origin)
summary(aov(response~soiltype*habitat+Error(destination+origin)))
anova(lme(response~soiltype*habitat,random=~1|destination/origin))
#
#"habitat" type is either 'arable' or 'grassland'
#"destination" indicates what site the soil was transplanted into, and is considered a random factor within habitat type
#"soiltype" is either 'arable' or 'grassland'
#"origin" indicates what site the soil was taken from, and is considered a random factor within soil type
#"response" is the response variable, typically some plant parameter such as growth rate or number of leaves, but in this example it is a random number between 0 and 1.
#
"habitat"	"destination"	"soiltype"	"origin"	"response"
1	1	1	1	0.63
1	2	1	1	0.76
1	3	1	1	0.14
2	4	1	1	0.27
2	5	1	1	0.88
2	6	1	1	0.41
1	1	1	2	0.47
1	2	1	2	0.48
1	3	1	2	0.76
2	4	1	2	0.83
2	5	1	2	0.88
2	6	1	2	0.57
1	1	1	3	0.80
1	2	1	3	0.31
1	3	1	3	0.22
2	4	1	3	0.53
2	5	1	3	0.97
2	6	1	3	0.30
1	1	2	4	0.46
1	2	2	4	0.99
1	3	2	4	0.56
2	4	2	4	0.32
2	5	2	4	0.46
2	6	2	4	0.64
1	1	2	5	0.03
1	2	2	5	0.41
1	3	2	5	0.24
2	4	2	5	0.60
2	5	2	5	0.04
2	6	2	5	0.30
1	1	2	6	0.97
1	2	2	6	0.60
1	3	2	6	0.22
2	4	2	6	0.16
2	5	2	6	0.58
2	6	2	6	0.21



-----Original Message-----
From: Spencer Graves [mailto:spencer.graves@pdf.com]
Sent: Sat 2006-07-22 20:03
To: ESCHEN Rene
Cc: Doran, Harold; r-help@stat.math.ethz.ch
Subject: Re: [R] Random structure of nested design in lme
 
	  Have you considered the following:

	  anova(lme(NA.1~soiltype*habitat,random=~1|destination/origin))

	  This seems more closely to match the 'aov' command in your original 
post.  This model might be written in more detail as follows:

	  NA.1[s, h, i,j,k] = b0 + ST[s] + H[h] +
		ST.H[s[i],j[j] j] + d[i] + o[i,j] + e[i,j,k]

where 	  b0 = a constant to be estimated,

	  s = the soil type for that particular sample,

	  h = the habitat for that sample,

	  ST = soil type coefficients to be estimated subject to a constraint 
that they sum to 0,

	  H = habitat coefficients to be estimated subject to the constraint 
that they sum to 0,

	  ST.H = soil type by habitat interaction coefficients to be estimated 
subject to constraints that ST.H[s,.] sum to 0 and ST.H[., h] also sum 
to 0,

	  d[i] = a random deviation associated with each destination, assuming 
the d's are all normal, independent, with mean 0 and unknown but 
constant variance s2.d

	  o[i, j] = a random deviation associated with each destination / 
origin combination, assuming the o's are all normal, independent, with 
mean 0 and unknown variance s2.o,

and 	  e[i,j,j] = the standard unknown noise term, normal, independent 
with mean 0 and unknown variance s2.e.

	  The model you wrote includes nested noise terms for soil type and 
habitat as well.  These terms are not estimable, which makes the answers 
garbage, but the 'lme' function does not check for replicates and 
therefore sometimes gives garbage answers without warning.

	  To get more information from the fit, I suggest you first try 
'methods(class="lme")', and review help pages associated with what you 
see listed there.

	  Have you looked at Pinheiro and Bates (2000) Mixed-Effects Models in 
S and S-Plus (Springer)?  This is my all-time favorite reference on 
Bates has been one of the leading original contributors in variance 
components analysis and nonlinear estimation more generally for over 25 
years.  The 'nlme' package is the product of his work and the work of 
many of his graduate students prior to 2000.  The book, at least from my 
perspective, is very well written.  Moreover, the standard R 
distribution includes files named "ch01.R", "ch02.R", ..., "ch06.R", 
"ch08.R" with the R scripts accompanying each chapter in the book in 
"~\library\nlme\scripts" under the R installation directory on your hard 
drive, e.g. "D:\Program files\R\R-2.3.1\library\nlme\scripts", on my 
computer.  There are minor changes in the syntax in a few places between 
the book and the current R implementation that make it impossible to get 
some of the published answers.  Using these script files increases the 
likelihood that you will get essentially the book's answers and won't be 
defeated by subtle typographical errors or by the difference between x^2 
and I(x^2), for example.

	  If you would like further information from this listserver, please 
submit another post, preferably including a "commented, minimal, 
self-contained, reproducible code", as suggested in the posting guide 
"www.R-project.org/posting-guide.html".

	  Hope this helps.
	  Spencer Graves

ESCHEN Rene wrote:
> Although I know it's not correct, this is what I tried in lme:
> 
> anova(lme(NA.1~soiltype*habitat,random=~1|destination/habitat/origin/soiltype))
> 
> #                 numDF denDF   F-value p-value
> #(Intercept)          1   130 12.136195  0.0007
> #soiltype             1   130 15.099792  0.0002
> #habitat              1    10  0.699045  0.4226
> #soiltype:habitat     1   130  2.123408  0.1475
> 
> René.
> 
> -----Original Message-----
> From: Doran, Harold [mailto:HDoran@air.org]
> Sent: Wed 2006-07-19 13:53
> To: ESCHEN Rene; r-help@stat.math.ethz.ch
> Subject: RE: [R] Random structure of nested design in lme
>  
> Can you provide an example of what you have done with lme so we might be able to evaluate the issue? 
> 
>> -----Original Message-----
>> From: r-help-bounces@stat.math.ethz.ch 
>> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of ESCHEN Rene
>> Sent: Wednesday, July 19, 2006 7:37 AM
>> To: r-help@stat.math.ethz.ch
>> Subject: [R] Random structure of nested design in lme
>>
>> All,
>>
>> I'm trying to analyze the results of a reciprocal transplant 
>> experiment using lme(). While I get the error-term right in 
>> aov(), in lme() it appears impossible to get as expected. I 
>> would be greatful for any help.
>>
>> My experiment aimed to identify whether two fixed factors 
>> (habitat type and soil type) affect the development of 
>> plants. I took soil from six random sites each of two types 
>> (arable and grassland) and transplanted them back into the 
>> sites of origin in such way that in each of the sites there 
>> were six pots containing arable soil and six pots of 
>> grassland soil, each containing a seedling.
>>
>> With aov(), I got the analysis as I expected, with habitat 
>> type tested against destination site, and soil type tested 
>> against origin site:
>>
>> summary(aov(response~soiltype*habitat+Error(destination+origin)))
>> #
>> #Error: destination
>> #          Df  Sum Sq Mean Sq F value Pr(>F)
>> #habitat    1  1.0000  1.0000   0.699 0.4226
>> #Residuals 10 14.3056  1.4306               
>> #
>> #Error: origin
>> #          Df  Sum Sq Mean Sq F value   Pr(>F)   
>> #soiltype   1 1.77778 1.77778  11.636 0.006645 **
>> #Residuals 10 1.52778 0.15278                    
>> #---
>> #Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #
>> #Error: Within
>> #                  Df  Sum Sq Mean Sq F value Pr(>F)
>> #soiltype:habitat   1  0.2500  0.2500  2.1774 0.1427
>> #Residuals        120 13.7778  0.1148     
>>
>> However, when I try to replicate this analysis in lme, I am 
>> unable to get the structure of the random factors (origin and 
>> destination) correct. Does anyone have a suggestion how to 
>> resolve this problem?
>>
>> Thanks in advance.
>>
>> René Eschen
>>
>> CABI Bioscience Centre Switzerland
>> Rue des Grillons 1
>> 2800 Delémont
>> Switzerland
>>
>> 	[[alternative HTML version deleted]]
>>
>>
> 
> 
> 	[[alternative HTML version deleted]]
> 
> 
> 
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> 
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