fastLm | R Documentation |
fastLm
estimates the linear model using one of several methods
implemented using the Eigen
linear algebra library.
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, ...)
y |
the response vector |
X |
a model matrix |
formula |
an object of class |
data |
an optional data frame, list or environment (or object
coercible by |
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 |
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.
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..
Eigen is described at http://eigen.tuxfamily.org/index.php?title=Main_Page. RcppEigen is written by Douglas Bates, Dirk Eddelbuettel and Romain Francois.
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
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
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