Uses flexible parametric additive models (see areg and its
use of regression splines), or alternatively to run a regular regression
after replacing continuous variables with ranks, to
determine how well each variable can be predicted from the remaining
variables. Variables are dropped in a stepwise fashion, removing the
most predictable variable at each step. The remaining variables are used
to predict. The process continues until no variable still in the list
of predictors can be predicted with an \(R^2\) or adjusted \(R^2\)
of at least r2 or until dropping the variable with the highest
\(R^2\) (adjusted or ordinary) would cause a variable that was dropped
earlier to no longer be predicted at least at the r2 level from
the now smaller list of predictors.
There is also an option qrank to expand each variable into two
columns containing the rank and square of the rank. Whenever ranks are
used, they are computed as fractional ranks for numerical reasons.
redun(formula, data=NULL, subset=NULL, r2 = 0.9,
type = c("ordinary", "adjusted"), nk = 3, tlinear = TRUE,
rank=qrank, qrank=FALSE,
allcat=FALSE, minfreq=0, iterms=FALSE, pc=FALSE, pr = FALSE, ...)
# S3 method for redun
print(x, digits=3, long=TRUE, ...)an object of class "redun"
a formula. Enclose a variable in I() to force
linearity. Alternately, can be a numeric matrix, in which case the
data are not run through dataframeReduce. This is useful when
running the data through transcan first for nonlinearly
transforming the data.
a data frame, which must be omitted if formula is a
matrix
usual subsetting expression
ordinary or adjusted \(R^2\) cutoff for redundancy
specify "adjusted" to use adjusted \(R^2\)
number of knots to use for continuous variables. Use
nk=0 to force linearity for all variables.
set to FALSE to allow a variable to be automatically
nonlinearly transformed (see areg) while being predicted. By
default, only continuous variables on the right hand side (i.e., while
they are being predictors) are automatically transformed, using
regression splines. Estimating transformations for target (dependent)
variables causes more overfitting than doing so for predictors.
set to TRUE to replace non-categorical varibles
with ranks before running the analysis. This causes nk to be
set to zero.
set to TRUE to also include squares of ranks to
allow for non-monotonic transformations
set to TRUE to ensure that all categories of
categorical variables having more than two categories are redundant
(see details below)
For a binary or categorical variable, there must be at
least two categories with at least minfreq observations or
the variable will be dropped and not checked for redundancy against
other variables. minfreq also specifies the minimum
frequency of a category or its complement
before that category is considered when allcat=TRUE.
set to TRUE to consider derived terms (dummy
variables and nonlinear spline components) as separate variables.
This will perform a redundancy analysis on pieces of the variables.
if iterms=TRUE you can set pc to TRUE
to replace the submatrix of terms corresponding to each variable
with the orthogonal principal components before doing the redundancy
analysis. The components are based on the correlation matrix.
set to TRUE to monitor progress of the stepwise algorithm
arguments to pass to dataframeReduce to remove
"difficult" variables from data if formula is
~. to use all variables in data (data must be
specified when these arguments are used). Ignored for print.
an object created by redun
number of digits to which to round \(R^2\) values when printing
set to FALSE to prevent the print method
from printing the \(R^2\) history and the original \(R^2\) with
which each variable can be predicted from ALL other variables.
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
A categorical variable is deemed
redundant if a linear combination of dummy variables representing it can
be predicted from a linear combination of other variables. For example,
if there were 4 cities in the data and each city's rainfall was also
present as a variable, with virtually the same rainfall reported for all
observations for a city, city would be redundant given rainfall (or
vice-versa; the one declared redundant would be the first one in the
formula). If two cities had the same rainfall, city might be
declared redundant even though tied cities might be deemed non-redundant
in another setting. To ensure that all categories may be predicted well
from other variables, use the allcat option. To ignore
categories that are too infrequent or too frequent, set minfreq
to a nonzero integer. When the number of observations in the category
is below this number or the number of observations not in the category
is below this number, no attempt is made to predict observations being
in that category individually for the purpose of redundancy detection.
areg, dataframeReduce,
transcan, varclus,
subselect::genetic
set.seed(1)
n <- 100
x1 <- runif(n)
x2 <- runif(n)
x3 <- x1 + x2 + runif(n)/10
x4 <- x1 + x2 + x3 + runif(n)/10
x5 <- factor(sample(c('a','b','c'),n,replace=TRUE))
x6 <- 1*(x5=='a' | x5=='c')
redun(~x1+x2+x3+x4+x5+x6, r2=.8)
redun(~x1+x2+x3+x4+x5+x6, r2=.8, minfreq=40)
redun(~x1+x2+x3+x4+x5+x6, r2=.8, allcat=TRUE)
# x5 is no longer redundant but x6 is
redun(~x1+x2+x3+x4+x5+x6, r2=.8, rank=TRUE)
redun(~x1+x2+x3+x4+x5+x6, r2=.8, qrank=TRUE)
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