[R] mixed model nested ANOVA (part two)

From: Stephen Cole <swbcole_at_gmail.com>
Date: Sun, 24 Feb 2008 11:40:55 -0400

First of all thank you for the responses. I appreciate the suggestions i have received thus far.

Just to reiterate

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 nested in location nested in region.

Also i have read in Quinn and Keough 2002, design and analysis of experiments for biologists, that a variance component analysis should only be conducted after a rejection of the null hypothesis of no variance at that level.

I have tried to implement
mod1<-lmer(density ~ 1 + (1|site) + (1|location) + (1|region))

However, as i understand it, this treats all my factors as random. Plus I do not know how to extract SS or MS from this model.

anova(mod1) gives me
Analysis of Variance Table

     Df Sum Sq Mean Sq

and summary(mod1) gives me
Linear mixed-effects model fit by REML
Formula: density ~ 1 + (1 | site) + (1 | location) + (1 | region)

   AIC BIC logLik MLdeviance REMLdeviance  15658 15678 -7825 15662 15650 Random effects:

 Groups   Name        Variance Std.Dev.
 site     (Intercept)  22191   148.97
 location (Intercept)  33544   183.15
 region   (Intercept)  41412   203.50
 Residual             696189   834.38

number of obs: 960, groups: site, 4; location, 4; region, 3

Fixed effects:

            Estimate Std. Error t value

(Intercept) 261.3 168.7 1.549

from what i understand the variance in the penultimate column are my variance components. But how do i conduct my significance test?

I have also tried
mod1<-lmer(density ~ region + (1|site) + (1|location))

Which i think is the correct mixed model for my design. However once again i do not know how to evaluate significance for the random factors.

Thank-you again for any additional advice i receive

Stephen Cole

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