## Continuing with the same example, I now show the full set of
contrasts and their
## associated regression coefficients. Remember that regression coefficients in
## models with factors are meaningful only when the dummy variables
are also displayed.
## construct full set of dummy variables to display all contrasts
sapply(threeway[,2:4], contrasts) ## default is treatment contrasts
contrasts(threeway$A) <- cbind(Lin=c(-1,0,1), Quad=c(1,-2,1))
contrasts(threeway$B) <- cbind(Lin=c(-1,0,1), Quad=c(1,-2,1))
contrasts(threeway$C) <- cbind(Lin=c(-1,1))
sapply(threeway[,2:4], contrasts) ## changed to orthogonal
## integer-valued polynomial contrasts
tw.aov <- aov(Y ~ A * B * C, data=threeway, x=TRUE)
x <- tw.aov$x ## dummy variables x
t(x)
anova(tw.aov)
beta.hat <- coef(tw.aov) ## regression coefficients beta.hat
## construct predicted values from beta.hat
y.hat <- x %*% beta.hat
y.hat
fitted(tw.aov) ## compare to predicted values from fitted function
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