lm.fit {stats}

Fitter Functions for Linear Models

Description

These are the basic computing engines called by lm used to fit linear models. These should usually not be used directly unless by experienced users. .lm.fit() is a bare-bones wrapper to the innermost QR-based C code, on which glm.fit and lsfit are also based, for even more experienced users.

Usage

lm.fit (x, y,    offset = NULL, method = "qr", tol = 1e-7,
       singular.ok = TRUE, ...)

lm.wfit(x, y, w, offset = NULL, method = "qr", tol = 1e-7,
        singular.ok = TRUE, ...)

.lm.fit(x, y, tol = 1e-7)

Arguments

x

design matrix of dimension n * p.

y

vector of observations of length n, or a matrix with n rows.

w

vector of weights (length n) to be used in the fitting process for the wfit functions. Weighted least squares is used with weights w, i.e., sum(w * e^2) is minimized.

offset

(numeric of length n). This can be used to specify an a priori known component to be included in the linear predictor during fitting.

method

currently, only method = "qr" is supported.

tol

tolerance for the qr decomposition. Default is 1e-7.

singular.ok

logical. If FALSE, a singular model is an error.

...

currently disregarded.

Details

If y is a matrix, offset can be a numeric matrix of the same dimensions, in which case each column is applied to the corresponding column of y.

Value

a list with components (for lm.fit and lm.wfit)

coefficients

p vector

residuals

n vector or matrix

fitted.values

n vector or matrix

effects

n vector of orthogonal single-df effects. The first rank of them correspond to non-aliased coefficients, and are named accordingly.

weights

n vector — only for the *wfit* functions.

rank

integer, giving the rank

df.residual

degrees of freedom of residuals

qr

the QR decomposition, see qr.

Fits without any columns or non-zero weights do not have the effects and qr components.

.lm.fit() returns a subset of the above, the qr part unwrapped, plus a logical component pivoted indicating if the underlying QR algorithm did pivot.

See Also

lm which you should use for linear least squares regression, unless you know better.

Examples

require(utils)
set.seed(129)

n <- 7 ; p <- 2
X <- matrix(rnorm(n * p), n, p) # no intercept!
y <- rnorm(n)
w <- rnorm(n)^2

str(lmw <- lm.wfit(x = X, y = y, w = w))

str(lm. <- lm.fit (x = X, y = y))

## fits w/o intercept:
all.equal(unname(coef(lm(y ~ X-1))),
          unname(coef( lm.fit(X,y))))
all.equal(unname(coef( lm.fit(X,y))),
                 coef(.lm.fit(X,y)))

if(require("microbenchmark")) {
  mb <- microbenchmark(lm(y~X-1), lm.fit(X,y), .lm.fit(X,y))
  print(mb)
  boxplot(mb, notch=TRUE)
}