These functions provide an alternative to the coding functions supplied
in the stats package, namely contr.treatment, contr.sum,
contr.helmert and contr.poly.
code_control(n, contrasts = TRUE, sparse = FALSE)code_control_last(n, contrasts = TRUE, sparse = FALSE)
code_diff(n, contrasts = TRUE, sparse = FALSE)
code_diff_forward(n, contrasts = TRUE, sparse = FALSE)
code_helmert(n, contrasts = TRUE, sparse = FALSE)
code_helmert_forward(n, contrasts = TRUE, sparse = FALSE)
code_deviation(n, contrasts = TRUE, sparse = FALSE)
code_deviation_first(n, contrasts = TRUE, sparse = FALSE)
code_poly(n, contrasts = TRUE, sparse = FALSE)
contr.diff(n, contrasts = TRUE, sparse = FALSE)
Either a positive integer giving the number of levels or the levels
attribute of a factor, supplying both the number of levels via its length and
labels potentially to be used in the dimnames of the result.
Logical: Do you want the \(n \times (n-1)\) coding
matrix (TRUE) or an \(n \times n\) full-rank matrix, (as is
sometimes needed by the fitting functions) (FALSE)?
Logical: Do you want the result to be a sparse matrix
object, as generated the the Matrix package?
A coding matrix, as requested by fitting functions using linear model formulae with factor predictors.
All functions with names of the form code_xxxx return
coding matrices which, in a simple model, make the intercept term
the simple ("unweighted") average of the class means. This can be
important in some non-standard ANOVA tables. The function
contr.diff is an exception, and is offered as a natural companion
to stats::contr.treatment, with which it is closely aligned.
Similar to contr.treatment, with
contrasts comparing the class means (the "treatments") with
the first class mean (the "control").
Similar to code_control, but using the final
class mean as the "control". Cf. contr.SAS
The contrasts are the successive differences of the treatment means,
\(\mu_{i+i} - \mu_i\). This coding function has no counterpart in the stats
package. It is suggested as an alternative to the default coding,
contr.poly, for
ordered factors. It offers a visual check of monotonicity of the class means
with the ordered levels of the factor. Unlike stats::contr.poly
there is no assumption that the factor levels
are in some sense "equally spaced".
Very similar to code_diff, but using forward
differences: \(\mu_i - \mu_{i+1}\)
Similar to contr.helmert, but with a
small scaling change to make the regression coefficients (i.e. the contrasts)
more easily interpretable. The contrasts now compare each class mean, starting
from the second, with the average of all class means coming prior to it in the
factor levels order.
Similar to code_helmert, but comparing each class
mean, up to the second last, with the average of all class means coming after it in
the factor levels order.
Similar to contr.sum, which is described
as having the "effects" summing to zero. A more precise description might be to
say that the contrasts are the deviations of each class mean from the average
of them, i.e. \(\mu_i - \bar\mu\). To avoid redundancy, the
last deviation is omitted.
Very similar to code_deviation, but omitting
the first deviation to avoid redundancy rather than the last.
Similar in effect to contr.poly but
for levels fewer than 15 using an unnormalized basis for the orthogonal polynomials
with integer entries. (Orthogonal polynomials were originally given in this form
as tables.) The only advantage over stats::contr.poly is one of display.
Use stats::contr.poly in preference other than for teaching purposes.
Very similar in effect to code_diff, yielding the same
differences as the contrasts, but like stats::contr.treatment using the
first class mean as the intercept coefficient rather than the simple average of
the class means, as with code_diff. Some would regard this as making it
unsuitable for use in some non-standard ANOVA tables.
The MASS function contr.sdif which is an early
version of code_deviation (by the same author).
# NOT RUN {
(M <- code_control(5))
mean_contrasts(M)
(M <- stats::contr.treatment(5))
mean_contrasts(M) ## same contrasts; different averaging vector.
mean_contrasts(stats::contr.helmert(6)) ## Interpretation obscure
mean_contrasts(code_helmert(6)) ## each mean with the average preceding
mean_contrasts(code_helmert_forward(6)) ## each mean with the averave succeeding
# }
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