# redun

##### Redundancy Analysis

Uses flexible parametric additive models (see `areg`

and its
use of regression splines) 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.

- Keywords
- multivariate, models, methods, regression, smooth

##### Usage

```
redun(formula, data=NULL, subset=NULL, r2 = 0.9,
type = c("ordinary", "adjusted"), nk = 3, tlinear = TRUE,
allcat=FALSE, minfreq=0, iterms=FALSE, pc=FALSE, pr = FALSE, ...)
# S3 method for redun
print(x, digits=3, long=TRUE, ...)
```

##### Arguments

- formula
a formula. Enclose a variable in

`I()`

to force linearity.- data
a data frame

- subset
usual subsetting expression

- r2
ordinary or adjusted \(R^2\) cutoff for redundancy

- type
specify

`"adjusted"`

to use adjusted \(R^2\)- nk
number of knots to use for continuous variables. Use

`nk=0`

to force linearity for all variables.- tlinear
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.- allcat
set to

`TRUE`

to ensure that all categories of categorical variables having more than two categories are redundant (see details below)- minfreq
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`

.- iterms
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.- pc
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.- pr
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`

.- x
an object created by

`redun`

- digits
number of digits to which to round \(R^2\) values when printing

- long
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.

##### 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.

##### Value

an object of class `"redun"`

##### See Also

`areg`

, `dataframeReduce`

,
`transcan`

, `varclus`

,
`subselect::genetic`

##### Examples

```
# NOT RUN {
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
# }
```

*Documentation reproduced from package Hmisc, version 4.3-0, License: GPL (>= 2)*