[R] FW: Re: Doubt about nested aov output
John Wilkinson (pipex)
wilks at dial.pipex.com
Wed Sep 7 16:30:24 CEST 2005
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
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