contrast example

nest_contrast.R

dd <- data.frame(A = factor(c(1,2,2,2)),
                 B = factor(1:4),
                 y = 1:4)
dd$i <- with(dd, factor(sprintf("A%d.B%d",A,B)))

## set up *inverse* contrast matrix
invc <- matrix(c(
    1/2, 1/6, 1/6, 1/6,  ## A-weighted mean
    -1, 1/3,  1/3, 1/3,  ## A1 vs A2 (== B1 vs mean{B2, B3, B4})
    0, 2/3, -1/3, -1/3,  ## B2 vs mean(B2, B3, B4)
    0, -1/3, 2/3, -1/3), ## B3 vs mean(B2, B3, B4)
    nrow = 4, byrow = 4,
    dimnames = list(c("int", "B.vs.A", "A1.vs.B2bar", "A2.vs.B2bar"),
                    dd$i))
print(invc, digits = 3)
##             A1.B1  A2.B2  A2.B3  A2.B4
## int           0.5  0.167  0.167  0.167
## B.vs.A       -1.0  0.333  0.333  0.333
## A1.vs.B2bar   0.0  0.667 -0.333 -0.333
## A2.vs.B2bar   0.0 -0.333  0.667 -0.333

## contrast matrix
zapsmall(solve(invc))
##       int B.vs.A A1.vs.B2bar A2.vs.B2bar
## A1.B1   1   -0.5           0           0
## A2.B2   1    0.5           1           0
## A2.B3   1    0.5           0           1
## A2.B4   1    0.5          -1          -1

contrasts(dd$i) <- solve(invc)[,-1] ## drop intercept
## (or could use -1 or +0 in the formula)
zapsmall(coef(lm(y~i, dd)))
##  (Intercept)      iB.vs.A iA1.vs.B2bar iA2.vs.B2bar
##            2            2           -1            0
## (numbers check out with hand calculation)