contrast
(Possibly Sparse) Contrast Matrices
Return a matrix of contrasts.
 Keywords
 regression, array, design
Usage
contr.helmert(n, contrasts = TRUE, sparse = FALSE)
contr.poly(n, scores = 1:n, contrasts = TRUE, sparse = FALSE)
contr.sum(n, contrasts = TRUE, sparse = FALSE)
contr.treatment(n, base = 1, contrasts = TRUE, sparse = FALSE)
contr.SAS(n, contrasts = TRUE, sparse = FALSE)
Arguments
 n
 a vector of levels for a factor, or the number of levels.
 contrasts
 a logical indicating whether contrasts should be computed.
 sparse
 logical indicating if the result should be sparse
(of class
dgCMatrix
), using package \href{https://CRAN.Rproject.org/package=#1}{\pkg{#1}}MatrixMatrix.  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
isFALSE
.
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 includes the 0degree, i.e.\ifelse{latex}{\out{~}}{ } constant,
polynomial when contrasts = FALSE
).
contr.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.
For consistency, sparse
is an argument to all these contrast
functions, however sparse = TRUE
for contr.poly
is typically pointless and is rarely useful for
contr.helmert
.
Value

A matrix with
n
rows and k
columns, with k=n1
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
Examples
library(stats)
(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
zapsmall(cP < contr.poly(3)) # Linear and Quadratic
zapsmall(crossprod(cP), digits = 15) # orthonormal up to fuzz