[R-sig-ME] Unbalanced nested design

[Stephen Cole]

Hello All - I would like to run a 2 factor nested ANOVA.  The design
is unbalanced as i have 6 sites in 3 regions and 3 sites in 1 other
region. Site is nested in region  I am interested in the differences
in mean recruit density among 4 regions.  I have used the lme function
in the nlme library and am confused about the output.  I have a copy
of P/B and I quote p. 25 " The lme function does produce sensible
maximum likelihood estimates or restricted maximum likelihood
estimates from the unbalanced data."  Thus, as i understand it lme can
handle this unbalanced data set that i have.  However, when i compared
the lme model to an aov model, the fixed effects results are
identical. (f-ratio and p-value).  How does lme handle unbalanced data
if the result is the same as aov which can not handle unbalanced data.
 Thank-you for any help provided.

I have attached a subsection of my data.  The total number of records
is 420, with a sample of 20 quadrat counts from each site (21 sites x
20 = 420)

Data:
          adults  recruits region site site2   site3
1      138 1268.3300    ANS    1     1    ANS:1
2      131  608.3300     ANS    1     1    ANS:1
3       13  696.8800     ANS    1     1    ANS:1
4       12  412.5000     ANS    1     1    ANS:1
5        2  355.5600     ANS    1     1    ANS:1
6        0  528.0000     ANS    1     1    ANS:1
7        4  421.2100     ANS    1     1    ANS:1
8        0  378.0000     ANS    1     1    ANS:1
9       92  893.3300    ANS    1     1    ANS:1
10      77 1184.3100   ANS    1     1    ANS:1
11      92  961.4200    ANS    1     1    ANS:1
12       0 1029.0000    ANS    1     1   ANS:1
13      19 1144.6800    ANS    1     1   ANS:1

Region (4 levels, fixed)
Site (6 levels and 3 levels, random)

data$site <- as.factor(data$site)
data$site3 <-factor(data$region:data$site)


mod.lme <- lme(recruits ~ region, data=data, random=~1|site3)

anova(mod)

            numDF denDF  F-value p-value
(Intercept)     1   399 93.58730  <.0001
region          3    17 19.21751  <.0001

 mod.aov <- aov(recruits ~ region + Error(site3), data=data)
 summary(mod.aov)\

Error: site3
                 Df   Sum Sq  Mean Sq F value    Pr(>F)
region        3  32024226 10674742  19.218 1.057e-05 ***
Residuals  17  9442984   555470
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Error: Within
                  Df   Sum Sq  Mean Sq F value Pr(>F)
Residuals  399 11839881    29674

Now, both F-ratios are 19.21, I am not sure what i am doing
incorrectly but I would appreciate any advice on my mistake.  Thanks
very much

Stephen Cole
Graduate student
Marine Ecology Lab
Saint Francis Xavier University