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, ...)
fastLm(X, y, method = 0L, ...)
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
X′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/.
See Also
lm, lm.fit
Examples
data(trees, package="datasets")
mm <- cbind(1, log(trees$Girth))
y <- log(trees$Volume)
flm <- fastLmPure(mm, y)
print(flm)
flmmod <- fastLm( log(Volume) ~ log(Girth), data=trees)
summary(flmmod)
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)
mm <- model.matrix(~ f1 * f2, dd)
kappa(mm)
set.seed(1)
dd$y <- mm %*% seq_len(ncol(mm)) + rnorm(nrow(mm), sd = 0.1)
summary(lm(y ~ f1 * f2, dd))
try(summary(fastLm(y ~ f1 * f2, dd)))