Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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\name{Design.trans}
\alias{Design.trans}
\alias{asis}
\alias{pol}
\alias{lsp}
\alias{rcs}
\alias{catg}
\alias{scored}
\alias{strat}
\alias{matrx}
\alias{\%ia\%}
\title{
Design Special Transformation Functions
}
\description{
This is a series of functions (\code{asis}, \code{pol}, \code{lsp}, \code{rcs}, \code{catg},
\code{scored}, \code{strat}, \code{matrx}, and \code{\%ia\%}) that set up special attributes
(such as
knots and nonlinear term indicators) that are carried through to fits
(using for example \code{lrm},\code{cph}, \code{ols}, \code{psm}). \code{anova.Design}, \code{summary.Design},
\code{plot.Design}, \code{survplot}, \code{fastbw}, \code{validate}, \code{specs},
\code{which.influence}, \code{nomogram.Design} and \code{latex.Design} use these
attributes to automate certain analyses (e.g., automatic tests of linearity
for each predictor are done by \code{anova.Design}). Many of the functions
are called implicitly. Some S functions such as \code{ns} derive data-dependent
transformations that are not "remembered" when predicted values are
later computed, so the predictions will be incorrect. The functions listed
here solve that problem.
\code{asis} is the identity transformation, \code{pol} is an ordinary (non-orthogonal) polynomial, \code{rcs} is
a linear tail-restricted cubic spline function (natural spline, for which the
\code{rcspline.eval} function generates the design matrix),
\code{catg} is for a categorical
variable, \code{scored} is for an ordered categorical
variable, \code{strat} is for a stratification factor
in a Cox model, \code{matrx} is for a matrix predictor, and \code{\%ia\%} represents
restricted interactions in which products involving nonlinear effects on both
variables are not included in the model. \code{asis, catg, scored, matrx} are seldom invoked
explicitly by the user (only to specify \code{label} or \code{name}, usually).
In the list below, functions \code{asis} through \code{strat} can have
arguments \code{x, parms, label, name} except that \code{parms} does not
apply to \code{asis, matrx, strat}.
}
\synopsis{
asis(\dots)
matrx(\dots)
pol(\dots)
lsp(\dots)
rcs(\dots)
catg(\dots)
scored(\dots)
strat(\dots)
\%ia\%(x1, x2)
}
\usage{
asis(x, parms, label, name)
matrx(x, label, name)
pol(x, parms, label, name)
lsp(x, parms, label, name)
rcs(x, parms, label, name)
catg(x, parms, label, name)
scored(x, parms, label, name)
strat(x, label, name)
\%ia\%(x1, x2)
}
\arguments{
\item{x}{
a predictor variable (or a function of one). If you specify e.g.
\code{pol(pmin(age,10),3)}, a cubic polynomial will be fitted in \code{pmin(age,10)}
(\code{pmin} is the S vector element--by--element function).
The predictor will be labeled \code{age} in the output, and plots with have
\code{age} in its original units on the axes. If you use a function such as
\code{pmin}, the predictor is taken as the first argument, and other arguments
must be defined in the frame in effect when predicted values, etc., are
computed.
}
\item{parms}{
parameters of transformation (e.g. number or location of knots).
For \code{pol} the argument is the order of the polynomial,
e.g. \code{2} for quadratic (the usual default). For \code{lsp} it is a
vector of knot locations (\code{lsp} will not estimate knot locations).
For \code{rcs} it is the
number of knots (if scalar), or vector of knot locations (if \code{>2} elements).
The default number is the \code{nknots} system option if \code{parms} is not given.
If the number of knots is given,
locations are computed for that number of knots.
For \code{catg}, \code{parms} is the
category labels (not needed if variable is an S category or factor variable). If
omitted, \code{catg} will use \code{unique(x)}, or \code{levels(x)} if \code{x} is a \code{category}
or a \code{factor}.
For \code{scored}, \code{parms} is a
vector of unique values of variable (uses \code{unique(x)} by default).
This is not needed if \code{x} is an S \code{ordered} variable.
For \code{strat}, \code{parms} is the category labels (not needed if variable is an S category variable). If
omitted, will use \code{unique(x)}, or \code{levels(x)} if \code{x} is
\code{category} or \code{factor}.
\code{parms} is not used for \code{matrix}.
}
\item{label}{
label of predictor for plotting (default = \code{"label"} attribute or variable
name)
}
\item{name}{
Name to use for predictor in model. Default is name of argument to
function
}
\item{x1}{}
\item{x2}{two continuous variables for which to form a
non-doubly-nonlinear interaction}
\item{\dots}{a variety of things}
}
\author{
Frank Harrell\cr
Department of Biostatistics, Vanderbilt University\cr
f.harrell@vanderbilt.edu
}
\seealso{
\code{\link[Hmisc]{rcspline.eval}}, \code{\link[Hmisc]{rcspline.restate}}, \code{\link{Design}}, \code{\link{cph}}, \code{\link{lrm}}, \code{\link{ols}}, \code{\link{datadist}}
}
\examples{
\dontrun{
options(knots=4, poly.degree=2)
country <- factor(country.codes)
blood.pressure <- cbind(sbp=systolic.bp, dbp=diastolic.bp)
fit <- lrm(Y ~ sqrt(x1)*rcs(x2) + rcs(x3,c(5,10,15)) +
lsp(x4,c(10,20)) + country + blood.pressure + poly(age,2))
# sqrt(x1) is an implicit asis variable, but limits of x1, not sqrt(x1)
# are used for later plotting and effect estimation
# x2 fitted with restricted cubic spline with 4 default knots
# x3 fitted with r.c.s. with 3 specified knots
# x4 fitted with linear spline with 2 specified knots
# country is an implied catg variable
# blood.pressure is an implied matrx variable
# since poly is not a Design function (pol is), it creates a
# matrx type variable with no automatic linearity testing
# or plotting
f1 <- lrm(y ~ rcs(x1) + rcs(x2) + rcs(x1) \%ia\% rcs(x2))
# \%ia\% restricts interactions. Here it removes terms nonlinear in
# both x1 and x2
f2 <- lrm(y ~ rcs(x1) + rcs(x2) + x1 \%ia\% rcs(x2))
# interaction linear in x1
f3 <- lrm(y ~ rcs(x1) + rcs(x2) + x1 \%ia\% x2)
# simple product interaction (doubly linear)
# Use x1 \%ia\% x2 instead of x1:x2 because x1 \%ia\% x2 triggers
# anova to pool x1*x2 term into x1 terms to test total effect
# of x1
}
}
\keyword{models}
\keyword{regression}
\keyword{math}
\keyword{manip}
\keyword{methods}
\keyword{survival}
\keyword{smooth}
\concept{logistic regression model}
\concept{transformation}