#### Demonstrate the difference between + , / and *.


#### Call the overall mean mu

mu <- 1
a <- 4
b <- 8
nreps <- 10

sigsqa <- 2
sigsqb <- 3

#### First we will do "+" --- the ADDITIVE model.

#### Factor 1 is "w" having "a" levels with sigmsqa = 2.

w <- rnorm(a) * sqrt(sigsqa)
names(w) <- paste("W",1:a,sep = "")


#### Factor 2 is "x" having "b" levels

x <- rnorm(b) * sqrt(sigsqb)
names(x) <- paste("X",1:b,sep = "")

#### The additive model says that muij = mu + wi + xj
#### So create the means like this

muij <- mu + rep(w,rep(b,a)) + rep(x,a)

muijk <- rep(muij,rep(nreps,a*b))
#### Take within group variance as 1.
data <- muijk + rnorm(a * b * nreps)

#### Create covariate columns

factor1 <- as.factor(rep(rep(names(w),rep(b,a)),rep(nreps,a*b)))
factor2 <- as.factor(rep(rep(names(x),a),rep(nreps,a*b)))

is.random(factor1) <- T
is.random(factor2) <- T

summary(varcomp(data ~ factor1 + factor2,method="ml"))
summary(raov(data ~ factor1 + factor2))

varcomp(data ~ factor1/factor2,method="ml")
summary(raov(data ~ factor1 / factor2))


varcomp(data ~ factor1*factor2,method="ml")
summary(raov(data ~ factor1*factor2))