contrast                package:stats                R Documentation

Contrast Matrices

Description:

     Return a matrix of contrasts.

Usage:

     contr.helmert(n, contrasts = TRUE)
     contr.poly(n, scores = 1:n, contrasts = TRUE)
     contr.sum(n, contrasts = TRUE)
     contr.treatment(n, base = 1, contrasts = TRUE)
     contr.SAS(n, contrasts = TRUE)

Arguments:

       n: a vector of levels for a factor, or the number of levels.

contrasts: a logical indicating whether contrasts should be computed.

  scores: the set of values over which orthogonal polynomials are to be
          computed.

    base: an integer specifying which group is considered the baseline
          group. Ignored if 'contrasts' is 'FALSE'.

Details:

     These functions are used for creating contrast matrices for use in
     fitting analysis of variance and regression models.  The columns
     of the resulting matrices contain contrasts which can be used for
     coding a factor with 'n' levels.  The returned value contains the
     computed contrasts.  If the argument 'contrasts' is 'FALSE' a
     square indicator matrix (the dummy coding) is returned *except*
     for 'contr.poly' (which include the 0-degree, i.e. constant,
     polynomial when 'contrasts = FALSE').

     'cont.helmert' returns Helmert contrasts, which contrast the
     second level with the first, the third with the average of the
     first two, and so on.  'contr.poly' returns contrasts based on
     orthogonal polynomials. 'contr.sum' uses 'sum to zero contrasts'.

     'contr.treatment' contrasts each level with the baseline level
     (specified by 'base'): the baseline level is omitted.  Note that
     this does not produce 'contrasts' as defined in the standard
     theory for linear models as they are not orthogonal to the
     intercept.

     'contr.SAS' is a wrapper for 'contr.treatment' that sets the base
     level to be the last level of the factor.  The coefficients
     produced when using these contrasts should be equivalent to those
     produced by many (but not all) SAS procedures.

Value:

     A matrix with 'n' rows and 'k' columns, with 'k=n-1' if
     'contrasts' is 'TRUE' and 'k=n' if 'contrasts' is 'FALSE'.

References:

     Chambers, J. M. and Hastie, T. J. (1992) _Statistical models._
     Chapter 2 of _Statistical Models in S_ eds J. M. Chambers and T.
     J. Hastie, Wadsworth & Brooks/Cole.

See Also:

     'contrasts', 'C', and 'aov', 'glm', 'lm'.

Examples:

     (cH <- contr.helmert(4))
     apply(cH, 2,sum) # column sums are 0!
     crossprod(cH) # diagonal -- columns are orthogonal
     contr.helmert(4, contrasts = FALSE) # just the 4 x 4 identity matrix

     (cT <- contr.treatment(5))
     all(crossprod(cT) == diag(4)) # TRUE: even orthonormal

     (cT. <- contr.SAS(5))
     all(crossprod(cT.) == diag(4))# TRUE

     (cP <- contr.poly(3)) # Linear and Quadratic
     zapsmall(crossprod(cP), digits=15) # orthonormal up to fuzz

