[R-sig-ME] most conservative df for mixed effects anova

Thierry Onkelinx th|erry@onke||nx @end|ng |rom |nbo@be
Wed Oct 16 09:31:14 CEST 2019

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
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel

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


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

> 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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