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

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

1	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 β from the least squares problem

β = argmin (z - Xβ)^T W (z- Xβ),

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

σ(x_i ; β) (1 - σ(x_i ; β)),

and z is the vector

z = X β + W^{-1} (y - σ(x_i ; β)).

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

β = (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