On 9/7/05, John Wilkinson (pipex) <wilks at dial.pipex.com>
wrote:> 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
The difference between models like
lmer(Glycogen~Treatment+(1|Rat)+(1|Rat:Liver))
and
lmer(Glycogen~Treatment+(1|Treatment:Rat)+(1|Treatment:Rat:Liver))
is more about the meaning of the levels of "Rat" than about the
meaning of "Treatment". As I understood it there are three different
rats labelled 1. There is a rat 1 on treatment 1 and a rat 1 on
treatment 2 and a rat 1 on treatment 3. Thus the levels of Rat do not
designate the "experimental unit", it is the levels of Treatment:Rat
that do this.