[Rd] generating contrast names

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From: John Fox (jfox@mcmaster.ca)
Date: Mon 02 Dec 2002 - 03:59:57 EST


Message-id: <5.1.0.14.2.20021201114748.01dcd870@mcmail.cis.mcmaster.ca>

Dear R-devel list members,

I'd like to suggest a more flexible procedure for generating contrast
names. I apologise for a relatively long message -- I want my proposal to
be clear.

I've never liked the current approach. For example, the names generated by
contr.treatment paste factor to level names with no separation between the
two; contr.sum simply numbers contrasts (I recall an exchange on the list
about this question); none of contr.* explicitly indicates what kind of
contrasts are generated. There are ways around these problems -- e.g.,
beginning level names with an uppercase character -- but in my experience
it's common to see things like "regionmidwest".

I propose that the current behaviour remain the default, but that the
contr.* functions use optional "prefix" and "suffix" characters around
level names (or their equivalent) and an optional identifier string to
indicate what kind of contrasts are generated. As well, I propose that
contr.sum optionally identify contrasts by level names. All of these
behaviours could be controlled by options which, if unset, would produce
the current behaviour. There might be problems with my implementation of
these ideas, or with the ideas themselves -- but I expect that these will
arise in discussion. (Of course, there's nothing to prevent me from using
the functions that I show below, but I thought that these questions might
be of more general interest.)

Here, for example, are rewrites of contr.treatment and contr.sum (renamed
contr.Treatment and contr.Sum because of name-space issues) that implement
my suggestions, together with illustrations of their use:

------------------------------------------------------------------------------------------------------------------------------

     contr.Treatment <- function (n, base = 1, contrasts = TRUE) {
         if (is.numeric(n) && length(n) == 1)
             levs <- 1:n
         else {
             levs <- n
             n <- length(n)
         }
         lev.opt <- getOption("decorate.factor.levels")
         pre <- if (is.null(lev.opt)) "" else lev.opt[1]
         suf <- if (is.null(lev.opt)) "" else lev.opt[2]
         dec <- getOption("decorate.contr.Treatment")
         dec <- if (is.null(dec)) "" else dec
         contr.names <- paste(pre, dec, levs, suf, sep="")
         contr <- array(0, c(n, n), list(levs, contr.names))
         diag(contr) <- 1
         if (contrasts) {
             if (n < 2)
                 stop(paste("Contrasts not defined for", n - 1, "degrees of
freedom"))
             if (base < 1 | base > n)
                 stop("Baseline group number out of range")
             contr <- contr[, -base, drop = FALSE]
         }
         contr
     }

     contr.Sum <- function (n, contrasts = TRUE)
     {
         if (length(n) <= 1) {
             if (is.numeric(n) && length(n) == 1 && n > 1)
                 levels <- 1:n
             else stop("Not enough degrees of freedom to define contrasts")
         }
         else levels <- n
         lenglev <- length(levels)
         lev.opt <- getOption("decorate.factor.levels")
         pre <- if (is.null(lev.opt)) "" else lev.opt[1]
         suf <- if (is.null(lev.opt)) "" else lev.opt[2]
         dec <- getOption("decorate.contr.Sum")
         dec <- if (is.null(dec)) "" else dec
         show.lev <- getOption("contr.Sum.show.levels")
         contr.names <- if ((!is.null(show.lev)) && show.lev) paste(pre,
dec, levels, suf, sep="")
         if (contrasts) {
             cont <- array(0, c(lenglev, lenglev - 1), list(levels,
                 contr.names[-lenglev]))
             cont[col(cont) == row(cont)] <- 1
             cont[lenglev, ] <- -1
         }
         else {
             cont <- array(0, c(lenglev, lenglev), list(levels, levels))
             cont[col(cont) == row(cont)] <- 1
         }
         cont
     }

> library(car)
        . . .

> data(Prestige)
> attach(Prestige)
> contrasts(type) <- "contr.Treatment"
>
> lm(prestige ~ (income + education)*type) # default behaviour

     Call:
     lm(formula = prestige ~ (income + education) * type)

     Coefficients:
         (Intercept) income education
typeprof typewc
             2.275753 0.003522 1.713275
15.351896 -33.536652
     income:typeprof income:typewc education:typeprof
education:typewc
             -0.002903 -0.002072 1.387809
4.290875

>
> options(decorate.factor.levels=c("[", "]")) # using brackets
> lm(prestige ~ (income + education)*type)

     Call:
     lm(formula = prestige ~ (income + education) * type)

     Coefficients:
             (Intercept) income education
     type[prof] type[wc]
                 2.275753 0.003522 1.713275
       15.351896 -33.536652
     income:type[prof] income:type[wc] education:type[prof]
education:type[wc]
             -0.002903 -0.002072 1.387809
     4.290875

>
> options(decorate.contr.Treatment="T.") # naming contrast type
> lm(prestige ~ (income + education)*type)

     Call:
     lm(formula = prestige ~ (income + education) * type)

     Coefficients:
             (Intercept) income education
         type[T.prof]
                 2.275753 0.003522 1.713275
             15.351896
                 type[T.wc] income:type[T.prof] income:type[T.wc]
  education:type[T.prof]
                 -33.536652 -0.002903 -0.002072
                1.387809
     education:type[T.wc]
                 4.290875

>
> options(decorate.contr.Treatment=NULL)
> options(decorate.factor.levels=c("#", "")) # alternate style, using hash
> lm(prestige ~ (income + education)*type)

     Call:
     lm(formula = prestige ~ (income + education) * type)

     Coefficients:
             (Intercept) income education
   type#prof type#wc
             2.275753 0.003522 1.713275
15.351896 -33.536652
     income:type#prof income:type#wc education:type#prof
education:type#wc
             -0.002903 -0.002072 1.387809
  4.290875

>
> lm(prestige ~ (income + education)*type,
contrasts=list(type="contr.Sum")) # default behaviour

     Call:
     lm(formula = prestige ~ (income + education) * type, contrasts =
list(type = "contr.Sum"))

     Coefficients:
         (Intercept) income education type1
        type2 income:type1 income:type2
         -3.785832 0.001864 3.606169 6.061585
  21.413481 0.001658 -0.001244
     education:type1 education:type2
         -1.892895 -0.505086

>
> options(contr.Sum.show.levels=TRUE)
> options(decorate.factor.levels=c("[", "]"))
> options(decorate.contr.Sum="S.") # showing levels, brackets,
contrast type
> lm(prestige ~ (income + education)*type,
contrasts=list(type="contr.Sum"))

     Call:
     lm(formula = prestige ~ (income + education) * type, contrasts =
list(type = "contr.Sum"))

     Coefficients:
             (Intercept) income education
           type[S.bc]
                 -3.785832 0.001864 3.606169
               6.061585
             type[S.prof] income:type[S.bc] income:type[S.prof]
  education:type[S.bc]
                 21.413481 0.001658 -0.001244
              -1.892895
     education:type[S.prof]
                 -0.505086

------------------------------------------------------------------------------------------------------------------------------

I look forward to people's comments.
  John
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox@mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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