[R] Extracting variance components from a Manova

[Charles Goodnight]

I am trying to run a simple nested manova with two levels of nesting, 
Sires, and Dams within Sires. The goal is to extract the among sires 
covariance matrix and secondarily, the among Dams within Sires 
covariance matrix. Both sires and dams are random effects. At present 
there are four dependent variables, but that may change. This is part of 
a larger bootstrapping project, so efficiency and the ability to 
automate the extraction are worth considering. Because it is a bootstrap 
computationally simpler approaches may be better, even if slightly 
biased (as long as the bias is consistent)

Two other important points. (1) We will be comparing the sire/dam data 
set to a similar data set that has only sires (dams have a single 
offspring, so “dams” becomes residuals). (2) The data are mildly 
unbalanced (one of the reasons for using a bootstrap approach). As a 
result of the differences in the structure of the two data sets and the 
unbalance using estimates of the variance components based on the sums 
of squares from summary.manova()$SS is leading to an unacceptably large 
bias. It is clear we need to use a better method (ReML?) to estimate the 
covariance matrices!

The code we use for running the manova:

Y <- cbind(Pupal_Mass, Dev_Time, Dry_Weight, Rel_Fitness)
sire <- factor(Sire)
dam<- factor(Dam)
fit <- manova(Y ~ sire + dam:sire)
sireSS <- summary(fit)$SS$sire
etc.

the sire covariance matrix = (MS(sires) – MS(dams)/(offspring/sire)
which gives us the correct answer with balanced data, but of course not 
with unbalanced data.

-- 
Charles Goodnight
Professor of Biology
University of Vermont
Burlington Vermont

802 656-8521