fastLm: Bare-bones linear model fitting function

In RcppArmadillo: 'Rcpp' Integration for the 'Armadillo' Templated Linear Algebra Library

Bare-bones linear model fitting function

Description

fastLm estimates the linear model using the solve function of Armadillo linear algebra library.

Usage

fastLmPure(X, y)

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

Arguments

y	a vector containing the explained variable.
X	a model matrix.
formula	a symbolic description of the model to be fit.
data	an optional data frame containing the variables in the model.
...	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 Armadillo library via the wrapper functions in the RcppArmadillo 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.

Lastly, one must be be careful in timing comparisons of lm and friends versus this approach based on Armadillo. The reason that Armadillo can do something like lm.fit faster than the functions in the stats package is because Armadillo uses the Lapack version of the QR decomposition while the stats package uses a modified Linpack version. Hence Armadillo uses level-3 BLAS code whereas the stats package uses level-1 BLAS. However, Armadillo will either fail or, worse, produce completely incorrect answers on rank-deficient model matrices whereas the functions from the stats package will handle them properly due to the modified Linpack code.

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 three components:

coefficients	a vector of coefficients
stderr	a vector of the (estimated) standard errors of the coefficient estimates
df.residual	a scalar denoting the degrees of freedom in the model

fastLm returns a richer object which also includes the residuals, fitted values and call argument similar to the lm or rlm functions..

Author(s)

Armadillo is written by Conrad Sanderson. RcppArmadillo is written by Romain Francois, Dirk Eddelbuettel, Douglas Bates and Binxiang Ni.

References

Armadillo project: https://arma.sourceforge.net/

See Also

lm, lm.fit

Examples

  
  data(trees, package="datasets")

  ## bare-bones direct interface
  flm <- fastLmPure( cbind(1, log(trees$Girth)), log(trees$Volume) )
  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 fastLm breaks 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
  summary(fastLm(y ~ f1 * f2, dd)) # some huge coefficients

  

RcppArmadillo documentation built on Sept. 12, 2024, 9:34 a.m.