irls.lr: Iteratively Re-weighted Least Squares
In dannyjameswilliams/danielR: Collection of Danny's R Code

irls.lr

R Documentation

Iteratively Re-weighted Least Squares

Optimisation procedure based on iteratively re-weighted least squares, called by lr.

irls.lr(y, x, init = NULL, tol = 1e-06, maxiter = 100)

`y`	response vector
`x`	model matrix of covariates
`init`	initial estimate of `theta`
`tol`	tolerance parameter, default `1e-6`
`maxiter`	optional number of iterations

Iterative method used to find parameter estimates of \beta from the least squares problem

\beta = argmin (z - X\beta)^T W (z- X\beta),

where W is a diagonal matrix of weights with i-th diagonal element being

\sigma(x_i ; \beta) (1 - \sigma(x_i ; \beta)),

and z is the vector

z = X \beta + W^{-1} (y - \sigma(x_i ; \beta)).

The parameter vector \beta is updated iteratively with a Newton update of the form

\beta = (X^T W X)^{-1} X^T W z.

a list containing

`par`	a vector of estimates of `theta`, the parameters being optimised
`val`	the value of the log-likelihood at the final `theta` estimate
`iters`	the number of iterations needed to converge