# Contrasts

##### Functions to Construct Contrasts

These are substitutes for similarly named functions in the stats package (note the uppercase letter starting the second word in each function name). The only difference is that the contrast functions from the car package produce easier-to-read names for the contrasts when they are used in statistical models.

The functions and this documentation are adapted from the stats package.

- Keywords
- models, regression

##### Usage

`contr.Treatment(n, base = 1, contrasts = TRUE)`contr.Sum(n, contrasts = TRUE)

contr.Helmert(n, contrasts = TRUE)

##### Arguments

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

- base
an integer specifying which level is considered the baseline level. Ignored if

`contrasts`

is`FALSE`

.- contrasts
a logical indicating whether contrasts should be computed.

##### 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`

then a square matrix is returned.

Several aspects of these contrast functions are controlled by options set via the `options`

command:

`decorate.contrasts`

This option should be set to a 2-element character vector containing the prefix and suffix characters to surround contrast names. If the option is not set, then

`c("[", "]")`

is used. For example, setting`options(decorate.contrasts=c(".", ""))`

produces contrast names that are separated from factor names by a period. Setting`options( decorate.contrasts=c("", ""))`

reproduces the behaviour of the R base contrast functions.`decorate.contr.Treatment`

A character string to be appended to contrast names to signify treatment contrasts; if the option is unset, then

`"T."`

is used.`decorate.contr.Sum`

Similar to the above, with default

`"S."`

.`decorate.contr.Helmert`

Similar to the above, with default

`"H."`

.`contr.Sum.show.levels`

Logical value: if

`TRUE`

(the default if unset), then level names are used for contrasts; if`FALSE`

, then numbers are used, as in`contr.sum`

in the`base`

package.

Note that there is no replacement for `contr.poly`

in the `base`

package (which produces
orthogonal-polynomial contrasts) since this function already constructs easy-to-read contrast names.

##### 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

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

##### See Also

##### Examples

```
# NOT RUN {
# contr.Treatment vs. contr.treatment in the base package:
lm(prestige ~ (income + education)*type, data=Prestige,
contrasts=list(type="contr.Treatment"))
## Call:
## lm(formula = prestige ~ (income + education) * type, data = Prestige,
## contrasts = list(type = "contr.Treatment"))
##
## Coefficients:
## (Intercept) income education
## 2.275753 0.003522 1.713275
## type[T.prof] type[T.wc] income:type[T.prof]
## 15.351896 -33.536652 -0.002903
## income:type[T.wc] education:type[T.prof] education:type[T.wc]
## -0.002072 1.387809 4.290875
lm(prestige ~ (income + education)*type, data=Prestige,
contrasts=list(type="contr.treatment"))
## Call:
## lm(formula = prestige ~ (income + education) * type, data = Prestige,
## contrasts = list(type = "contr.treatment"))
##
## Coefficients:
## (Intercept) income education
## 2.275753 0.003522 1.713275
## typeprof typewc income:typeprof
## 15.351896 -33.536652 -0.002903
## income:typewc education:typeprof education:typewc
## -0.002072 1.387809 4.290875
# }
```

*Documentation reproduced from package car, version 3.0-5, License: GPL (>= 2)*