Logistic regression

Maximum likelihood for a 0/1 outcome and a logit link, by Newton's method on the design with centred columns, the method glm() uses with family = binomial() when the columns are not collinear. Standard errors come from the inverse Fisher information.

Usage

lgtreg(x, y, tol = 1e-10, maxit = 50)

Arguments

x

The predictors: a numeric matrix with more rows than columns plus one, with no missing values; an intercept is always added.

y

The outcome: 0 or 1, one per row of x, both present.

tol

Newton steps stop when none moves a coefficient by more than tol (1 + |coefficient|): one positive number.

maxit

The most Newton steps: one whole number.

Value

A list: coef and se, named numeric vectors with the intercept first, and dev, the residual deviance.

References

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall. doi:10.1007/978-1-4899-3242-6

Examples

set.seed(1)
x <- matrix(rnorm(300 * 2), 300)
y <- rbinom(300, 1, plogis(0.5 + x[, 1] - x[, 2]))
lgtreg(x, y)$coef
#> (Intercept)          x1          x2 
#>   0.4864763   1.0070780  -0.8877568