| contrast {stats} | R Documentation |
(Possibly Sparse) Contrast Matrices
Description
Return a matrix of contrasts.
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 |
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 |
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 0-degree, i.e. constant,
polynomial when contrasts = FALSE).
contr.helmert returns \IHelmert 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=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
zapsmall(cP <- contr.poly(3)) # Linear and Quadratic
zapsmall(crossprod(cP), digits = 15) # orthonormal up to fuzz