# fastLm: Bare-bones linear model fitting function In RcppEigen: 'Rcpp' Integration for the 'Eigen' Templated Linear Algebra Library

 fastLm R Documentation

## Bare-bones linear model fitting function

### Description

fastLm estimates the linear model using one of several methods implemented using the Eigen linear algebra library.

### Usage

fastLmPure(X, y, method = 0L)
fastLm(X, ...)
## Default S3 method:
fastLm(X, y, method = 0L, ...)
## S3 method for class 'formula'
fastLm(formula, data = list(), method = 0L, ...)


### Arguments

 y the response vector X a model matrix formula an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given in the ‘Details’ section of the documentation for lm. data an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called. method an integer scalar with value 0 for the column-pivoted QR decomposition, 1 for the unpivoted QR decomposition, 2 for the LLT Cholesky, 3 for the LDLT Cholesky, 4 for the Jacobi singular value decomposition (SVD) and 5 for a method based on the eigenvalue-eigenvector decomposition of \mathbf{X}^\prime\mathbf{X}. Default is zero. ... not used

### Details

Linear models should be estimated using the lm function. In some cases, lm.fit may be appropriate.

The fastLmPure function provides a reference use case of the Eigen C++ template library via the wrapper functions in the RcppEigen package.

The fastLm function provides a more standard implementation of a linear model fit, offering both a default and a formula interface as well as print, summary and predict methods.

Internally the fastLm function, by default, uses a QR decomposition with column pivots, which is a rank-revealing decomposition, so that it can handle rank-deficient cases effectively. Other methods for determining least squares solutions are available according to the value of the method argument.

An example of the type of situation requiring extra care in checking for rank deficiency is a two-way layout with missing cells (see the examples section). These cases require a special pivoting scheme of “pivot only on (apparent) rank deficiency” which is not part of conventional linear algebra software.

### Value

fastLmPure returns a list with several components:

 coefficients a vector of coefficients se a vector of the standard errors of the coefficient estimates rank a scalar denoting the computed rank of the model matrix df.residual a scalar denoting the degrees of freedom in the model residuals the vector of residuals s a numeric scalar - the root mean square for residuals fitted.values the vector of fitted value

fastLm returns a richer object which also includes the call argument similar to the lm or rlm functions..

### Author(s)

Eigen is described at http://eigen.tuxfamily.org/index.php?title=Main_Page. RcppEigen is written by Douglas Bates, Dirk Eddelbuettel and Romain Francois.

### References

Douglas Bates and Dirk Eddelbuettel (2013). Fast and Elegant Numerical Linear Algebra Using the RcppEigen Package. Journal of Statistical Software, 52(5), 1-24. URL http://www.jstatsoft.org/v52/i05/.

lm, lm.fit

### Examples

  data(trees, package="datasets")
mm <- cbind(1, log(trees$Girth)) # model matrix y <- log(trees$Volume)            # response

## bare-bones direct interface
flm <- fastLmPure(mm, y)
print(flm)

## standard R interface for formula or data returning object of class fastLm
flmmod <- fastLm( log(Volume) ~ log(Girth), data=trees)
summary(flmmod)

## case where non-rank-revealing methods break down
dd <- data.frame(f1 = gl(4, 6, labels = LETTERS[1:4]),
f2 = gl(3, 2, labels = letters[1:3]))[-(7:8), ]
xtabs(~ f2 + f1, dd)     # one missing cell
mm <- model.matrix(~ f1 * f2, dd)
kappa(mm)                # large, indicating rank deficiency
set.seed(1)
dd\$y <- mm %*% seq_len(ncol(mm)) + rnorm(nrow(mm), sd = 0.1)
summary(lm(y ~ f1 * f2, dd))     # detects rank deficiency
try(summary(fastLm(y ~ f1 * f2, dd))) # also detects rank deficiency


RcppEigen documentation built on Sept. 11, 2024, 7:17 p.m.