# Re: [R] Mixed model Nested ANOVA

From: jebyrnes <jebyrnes_at_ucdavis.edu>
Date: Fri, 22 Feb 2008 15:34:11 -0800 (PST)

So, Site is nested in location. Location is nested in Region. And you are looking at how density varies. Let's think about this from the point of view of a model with varying intercepts.

You have some mean density in your study. That mean will deviate by site, location, and region. Each of which is nested in the other. So.

density ~ N(site mean, within site sd)
site mean ~ N(location mean, between site SD) location mean ~ N(region mean, between location SD) region mean ~ N(0, between region SD)

This last one may seem odd, but you can see it if you think about, say, location mean = region mean + N(0, between location SD), or, similarly, density = site mean + N(0, within site sd)

This can be fit in lmer with the following (I believe) mod1<-lmer(density ~ 1 + (1|site) + (1|location) + (1|region))

You can then use other methods described previously in the thread for post-hoc analysis. You can also use the arm library and look at ranef(mod1) and se.ranef(mod1) to look at the coefficient estimates and error for each level. I often find it helpful to look at an estimate +/- 2SE.

The nesting of location within region, site within location, etc, should take care of itself. See R news 2005 issue 1 page 29 http://www.r-project.org/doc/Rnews/Rnews_2005-1.pdf

-Jarrett

Stephen Cole-2 wrote:
>
> hello R help
>
> I am trying to analyze a data set that has been collected from a
> hierarchical sampling design. The model should be a mixed model nested
> ANOVA. The purpose of my study is to analyze the variability at each
> spatial scale in my design (random factors, variance components), and say
> something about the variability between regions (fixed factor, contrast of
> means). The data is as follows;
>
> region (fixed)
> Location (random)
> Site(random)
>
> site nested in location nested in region.
>
> I would like to run this as an ANOVA and then compute variance components.
>
> My question is when i use the aov command; mod1 <- aov(density ~
> region/location/site)
> is there any way to tell R which factor is random and fixed.
>
> I know i can specify fixed and random factors using lme or lmer but these
> methods do not allow me to extract an anova table (or do they?)
> I know that the data can be analyzed using a nested ANOVA because i have
> based my design on several papers in the marine biological literature
> (MEPS). Thank-you for any advice in advance.

>
> Stephen Cole
>
> [[alternative HTML version deleted]]
>
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Received on Fri 22 Feb 2008 - 23:41:49 GMT

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