[R] Conservative "ANOVA tables" in lmer

Martin Henry H. Stevens hstevens at muohio.edu
Thu Sep 7 13:46:24 CEST 2006

Dear lmer-ers,
My thanks for all of you who are sharing your trials and tribulations  

I was hoping to elicit some feedback on my thoughts on denominator  
degrees of freedom for F ratios in mixed models. These thoughts and  
practices result from my reading of previous postings by Doug Bates  
and others.

- I start by assuming that the appropriate denominator degrees lies  
between n - p and and n - q, where n=number of observations, p=number  
of fixed effects (rank of model matrix X), and q=rank of Z:X.
- I then conclude that good estimates of P values on the F ratios lie  
between 1 - pf(F.ratio, numDF, n-p) and 1 - pf(F.ratio, numDF, n-q).
- I further surmise that the latter of these (1 - pf(F.ratio, numDF,  
n-q)) is the more conservative estimate.

When I use these criteria and compare my "ANOVA" table to the results  
of analysis of Helmert contrasts using MCMC sample with highest  
posterior density intervals, I find that my conclusions (e.g. factor  
A, with three levels, has a "significant effect" on the response  
variable) are qualitatively the same.



Dr. Hank Stevens, Assistant Professor
338 Pearson Hall
Botany Department
Miami University
Oxford, OH 45056

Office: (513) 529-4206
Lab: (513) 529-4262
FAX: (513) 529-4243
"E Pluribus Unum"

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