G2SWEEP: Generalized inverse matrix of type 2 for linear regression
In sasLM: 'SAS' Linear Model

G2SWEEP

R Documentation

Generalized inverse matrix of type 2 for linear regression

Description

Generalized inverse is usually not unique. Some programs use this algorithm to get a unique generalized inverse matrix.

Usage

  G2SWEEP(A, Augmented=FALSE, eps=1e-08)

Arguments

`A`	a matrix to be inverted. If `A` is not a square matrix, G2SWEEP calls g2inv function.
`Augmented`	If this is `TRUE` and `A` is a model(design) matrix X, the last column should be X'y, the last row y'X, and the last cell y'y. See the reference and example for the detail. If the input matrix `A` is not a square matrix, `Augmented` option cannot be TRUE.
`eps`	Less than this value is considered as zero.

Details

Generalized inverse of g2-type is used by some softwares to do linear regression. See 'SAS Technical Report R106, The Sweep Operator: Its importance in Statistical Computing' by J. H. Goodnight for the detail.

Value

`when Augmented=FALSE`	ordinary g2 inverse
`when Augmented=TRUE`	g2 inverse and beta hats in the last column and the last row, and sum of square error (SSE) in the last cell
`attribute "rank"`	the rank of input matrix

Author(s)

Kyun-Seop Bae k@acr.kr

Examples

  f1 = uptake ~ Type + Treatment # formula
  x = ModelMatrix(f1, CO2)  # Model matrix and relevant information
  y = model.frame(f1, CO2)[, 1] # observation vector
  nc = ncol(x$X) # number of columns of model matrix
  XpY = crossprod(x$X, y)
  aXpX = rbind(cbind(crossprod(x$X), XpY), cbind(t(XpY), crossprod(y)))
  ag2 = G2SWEEP(aXpX, Augmented=TRUE)
  b = ag2[1:nc, (nc + 1)] ; b # Beta hat
  iXpX = ag2[1:nc, 1:nc] ; iXpX # g2 inverse of X'X
  SSE = ag2[(nc + 1), (nc + 1)] ; SSE # Sum of Square Error
  DFr = nrow(x$X) - attr(ag2, "rank") ; DFr # Degree of freedom for the residual

# Compare the below with the above
  REG(f1, CO2)
  aov1(f1, CO2)

sasLM documentation built on Oct. 2, 2024, 9:06 a.m.