[R] FW: Re: Doubt about nested aov output

[John Wilkinson (pipex)]

Ronaldo,

Further to my previous posting  on your Glycogen nested aov model.

Having read Douglas Bates' response and  Reflected on his lmer analysis
output of your aov nested model example as given.The Glycogen treatment has
to be a Fixed Effect.If a 'treatment' isn't a Fixed Effect what is ? If
Douglas Bates' lmer model is modified to treat Glycogen Treatment as a
purely Fixed Effect,with Rat and the interaction Rat:Liver as random effects
then--

> model.lmer<-lmer(Glycogen~Treatment+(1|Rat)+(1|Rat:Liver))
> summary(model.lmer)
Linear mixed-effects model fit by REML
Formula: Glycogen ~ Treatment + (1 | Rat) + (1 | Rat:Liver)
     AIC      BIC    logLik MLdeviance REMLdeviance
 239.095 248.5961 -113.5475   238.5439      227.095
Random effects:
 Groups    Name        Variance   Std.Dev.
 Rat:Liver (Intercept) 2.1238e-08 0.00014573
 Rat       (Intercept) 2.0609e+01 4.53976242
 Residual              4.2476e+01 6.51733769
# of obs: 36, groups: Rat:Liver, 6; Rat, 2

Fixed effects:
            Estimate Std. Error DF t value  Pr(>|t|)
(Intercept) 140.5000     3.7208 33 37.7607 < 2.2e-16 ***
Treatment2   10.5000     2.6607 33  3.9463 0.0003917 ***
Treatment3   -5.3333     2.6607 33 -2.0045 0.0532798 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:
           (Intr) Trtmn2
Treatment2 -0.358
Treatment3 -0.358  0.500

> anova(model.lmer)
Analysis of Variance Table
          Df  Sum Sq Mean Sq   Denom F value    Pr(>F)
Treatment  2 1557.56  778.78   33.00  18.335 4.419e-06 ***
 --------------------------------------------------------
which agrees with the aov model below.

>  model <- aov(Glycogen~Treatment+Error(Rat/Liver))
> summary(model)


John

-----Original Message-----
From: John Wilkinson (pipex) [mailto:wilks at dial.pipex.com]
Sent: 07 September 2005 12:04 PM
To: "Ronaldo Reis-Jr."
Cc: r-help
Subject: Re: [R] Doubt about nested aov output


Ronaldo ,

It looks as though you have specified your model incorrectly.

In the Rats example ,the Treatment is the only fixed effect,Rat and Liver
are random effects

In aov testing for sig of 'Means' of Random Effects is pointless and that is
why 'p' values are not given.Further more the interaction between a Random
Effect and a Fixed Effect is also a Random Effect. The 'aov' with error
structure terms output reflects this by only giving 'p' values to
Fixed Effects and their interactions

>  model <- aov(Glycogen~Treatment+Error(Rat/Liver))
> summary(model)

Error: Rat
          Df Sum Sq Mean Sq F value Pr(>F) #Rat is random effect
Residuals  1 413.44  413.44

Error: Rat:Liver				      #Rat:Liver is Random effect
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  4 164.444  41.111

Error: Within
          Df  Sum Sq Mean Sq F value    Pr(>F)
Treatment  2 1557.56  778.78  18.251 8.437e-06 *** #Fixed effect
Residuals 28 1194.78   42.67
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



I hope that this is of help.

John