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[S] What is residual error in a saturated model fit with lme?

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Subject: [S] What is residual error in a saturated model fit with lme?
From: Francis_Bruey@cytec.com
Date: Tue, 21 Sep 1999 09:21:59 -0400
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     All:
     
     Consider the following experiment:
     
     Factor A with 8 levels applied to 24 experimental units (3 per 
     level) in completely randomized fashion.
     
     Each unit is measured at 4 stages (initially and then after each of 
     3 consecutive applications of a standardized stress). 
     
     Dataframe has 96 rows, with columns Y (numeric response), uniq.unit 
     (factor, unique unit identifier), A (factor), and stage (factor).
     
     Fit with aov() using model:
     
        aov(Y ~ (A/uniq.unit)*stage)
     
     has zero residual error.
     
     Fit with lme() using model:
     
        lme(fixed = Y ~ A*stage, ran = ~ stage | uniq.unit)
     
     has nonzero residual error.  Is this model not saturated (am I 
     misunderstanding lme syntax)?  If it is saturated, what is the 
     residual error estimating?
     
     Using S-Plus 2000 on PC with Win95.  
     
     Thanks,
     Francis Bruey
     Francis_Bruey@st.cytec.com
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