redun: Redundancy Analysis

Description

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.

Usage

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, ...)

Arguments

Value

an object of class "redun" including an element "scores", a numeric matrix with all transformed values when each variable was the dependent variable and the first canonical variate was computed

Details

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.

Examples

Run this code

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)

# To help decode which variables made a particular variable redundant:
# r <- redun(...)
# r2describe(r$scores)