R: Fits Least Angle Regression, Lasso and Infinitesimal Forward...

lars {lars} | R Documentation

## Fits Least Angle Regression, Lasso and Infinitesimal Forward Stagewise regression models

### Description

These are all variants of Lasso, and provide the entire sequence of coefficients and fits, starting from zero, to the least squares fit.

### Usage

    lars(x, y, type = c("lasso", "lar", "forward.stagewise", "stepwise"),
        trace = FALSE, normalize = TRUE, intercept = TRUE, Gram, eps = .Machine$double.eps, max.steps, use.Gram = TRUE)

### Arguments

`x` | matrix of predictors
`y` | response
`type` | One of "lasso", "lar", "forward.stagewise" or "stepwise". The names can be abbreviated to any unique substring. Default is "lasso".
`trace` | If TRUE, lars prints out its progress
`normalize` | If TRUE, each variable is standardized to have unit L2 norm, otherwise it is left alone. Default is TRUE.
`intercept` | if TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included. Default is TRUE.
`Gram` | The X'X matrix; useful for repeated runs (bootstrap) where a large X'X stays the same.
`eps` | An effective zero
`max.steps` | Limit the number of steps taken; the default is `8 * min(m, n-intercept)`, with m the number of variables, and n the number of samples. For `type="lar"` or `type="stepwise"`, the maximum number of steps is `min(m,n-intercept)`. For `type="lasso"` and especially `type="forward.stagewise"`, there can be many more terms, because although no more than `min(m,n-intercept)` variables can be active during any step, variables are frequently droppped and added as the algorithm proceeds. Although the default usually guarantees that the algorithm has proceeded to the saturated fit, users should check.
`use.Gram` | When the number m of variables is very large, i.e. larger than N, then you may not want LARS to precompute the Gram matrix. Default is use.Gram=TRUE

### Details

LARS is described in detail in Efron, Hastie, Johnstone and Tibshirani (2002). With the "lasso" option, it computes the complete lasso solution simultaneously for ALL values of the shrinkage parameter in the same computational cost as a least squares fit. A "stepwise" option has recently been added to LARS.

### Value

A "lars" object is returned, for which print, plot, predict, coef and summary methods exist.

### Author(s)

Brad Efron and Trevor Hastie

### References

Efron, Hastie, Johnstone and Tibshirani (2003) "Least Angle Regression" (with discussion) Annals of Statistics; see also http://www-stat.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf. Hastie, Tibshirani and Friedman (2002) Elements of Statistical Learning, Springer, NY.

### See Also

print, plot, summary and predict methods for lars, and cv.lars

### Examples

    data(diabetes)
    par(mfrow=c(2,2))
    attach(diabetes)
    object <- lars(x,y)
    plot(object)
    object2 <- lars(x,y,type="lar")
    plot(object2)
    object3 <- lars(x,y,type="for") # Can use abbreviations
    plot(object3)
    detach(diabetes)

[Package lars version 1.2 Index]