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most conservative df for mixed effects anova (Carrie Perkins)

Nik Tuzov 
Hello Carrie:
Strictly speaking, the term conservative or aggressive should apply to the p-values rather than to the degrees of freedom.I assume you are asking what approach generates the largest p-value for your fixed effect of interest.In theory, one can't answer that question in advance.??
If methods X and Y result in n and m df for the error term, where n > m, it doesn't imply that X will produce a smaller p-value than Y,even though it's often in case in practice.
That being said, a method that is likely to be conservative should have df <= (count of experimental units less the count of fixedparameters in the model) <= (count of experimental units less one).
Regards,Nik Tuzov
On Wednesday, October 16, 2019, 5:02:31 AM CDT, r-sig-mixed-models-request at r-project.org <r-sig-mixed-models-request at r-project.org> wrote:
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Today's Topics:

? 1. most conservative df for mixed effects anova (Carrie Perkins)
? 2. Re: most conservative df for mixed effects anova
? ? ? (Thierry Onkelinx)

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Message: 1
Date: Tue, 15 Oct 2019 09:12:54 -0400
From: Carrie Perkins <cperk at terpmail.umd.edu>
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] most conservative df for mixed effects anova
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Hello!

I have data from an experiment and would like to run an anova with fixed
and random effects in R. Here is information on the data:

In the experiment, 3 replicates of 48 plant genotypes were planted into
each of 4 salinity treatments. This resulted in a total of 144 individuals
per treatment, amounting to a grand total of 576 individuals in the whole
experiment. Within each treatment, random sets of 24 plants were grouped
into a total of 6 pools to make it easier to monitor salinity levels. I
would like to model these pools as random Experimental Units.

I would like to make Experimental Unit the random effect and look at the
treatment X genotype interaction as fixed effects.

lmer_model_3 <- aov(Y~Genotype*Treatment + Error(1|Experimental Unit),
data=dataframe)

What would be the most conservative method for calculating degrees of
freedom for the random effects term of an anova? When I've tried
researching this question online, I find a lot of information on
calculating degrees of freedom for basic 1- and 2-way anovas (which I
understand) but I can't find clear guidance on how to calculate the degrees
of freedom for anovas with random effects.

Thank you!

Sincerely,
Carrie Perkins

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Message: 2
Date: Wed, 16 Oct 2019 09:31:14 +0200
From: Thierry Onkelinx <thierry.onkelinx at inbo.be>
To: Carrie Perkins <cperk at terpmail.umd.edu>
Cc: r-sig-mixed-models <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] most conservative df for mixed effects anova
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Content-Type: text/plain; charset="utf-8"

Dear Carrie,

The most conservative number IMHO is the sum of the number fixed effects
parameters and the number of random effects parameters (in case of a random
intercept: 1 level = 1 parameter). Het most liberate number would replace
the number random effects parameters with the number of random effect
hyperparameters (a random intercept = 1 variance = 1 hyperparameter).

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
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<https://www.inbo.be>


Op di 15 okt. 2019 om 15:20 schreef Carrie Perkins <cperk at terpmail.umd.edu>:
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