R: Fitter Functions for Linear Models

lm.fit {stats}

R Documentation

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.

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)
}

[Package stats version 4.4.1 Index]