Helmert

Helmert contrasts. Compares categories of an independent variable with the mean of the subsequent categories. The general matrix form is

   mean (1/k       1/k   ...       1/k       1/k       1/k)
  df(1) (  1  -1/(k-1)   ...  -1/(k-1)  -1/(k-1)  -1/(k-1))
  df(2) (  0         1   ...  -1/(k-2)  -1/(k-2)  -1/(k-2))
      .              .
      .              .
df(k-2) (  0         0   ...         1      -1/2      -1/2)
df(k-1) (  0         0   ...         0         1        -1)

where k is the number of categories of the independent variable. For example, an independent variable with four categories has a Helmert contrast matrix of the following form:

(1/4   1/4   1/4   1/4)
(  1  -1/3  -1/3  -1/3)
(  0     1  -1/2  -1/2)
(  0     0     1    -1)