# Contrasts

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Percentile

##### 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: [object Object],[object Object],[object Object],[object Object],[object Object] 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. (2011) An R Companion to Applied Regression, Second Edition, Sage.

contr.treatment, contr.sum, contr.helmert, contr.poly

##### Aliases
• Contrasts
• contr.Treatment
• contr.Sum
• contr.Helmert
##### Examples
# 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 2.0-11, License: GPL (>= 2)

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