firthglm.fit {mbest}

Fitting Generalized Linear Models with Firth's Bias Reduction

Description

A drop-in replacement for glm.fit which uses Firth's bias-reduced estimates instead of maximum likelihood.

Usage

firthglm.fit(x, y, weights = rep(1, nobs),
             start = NULL, etastart = NULL, mustart = NULL,
             offset = rep(0, nobs), family = gaussian(),
             control = list(...), intercept = TRUE, singular.ok = TRUE, ...)

firthglm.control(epsilon = 1e-8, maxit = 25, qr.tol = 1e-7,
                 improve.tol = 1e-4, curvature.tol = 0.9,
                 linesearch.method = "linesearch",
                 linesearch.maxit = 20, trace = FALSE)

Arguments

x, y, weights, start, etastart, mustart, offset, family, control, intercept, singular.ok, ...

arguments that have the same functions as for glm.fit.

qr.tol

tolerance parameter for determining the rank of x.

epsilon, maxit

convergence parameters for the quasi-Newton method.

linesearch.method

line search methods (one of "linesearch", "backtrack", or "blindsearch")

improve.tol, curvature.tol, linesearch.maxit

tolerance parameters for the linesearch procedure.

trace

logical indicating if output should be produced for each iteration.

Details

Firth's modified score function gives rise to estimates with smaller biases than their maximum likelihood counterparts. Unlike the maximum likelihood estimates, if the design matrix is of full rank, then the Firth bias-reduced estimate is finite.

By default, the fitting procedure uses a quasi-Newton optimization method, with a More-Thuente linesearch.

Value

firthglm.fit returns an object having the same components that a call to glm.fit would produce.

Note

Currently, only families with canonical link functions are supported.

Author(s)

Patrick O. Perry

References

Firth, D. (1993) Bias reduction of maximum likelihood estimates. Biometrika 80, 27-–38.

More, J. J. and Thuente, D. J. (1994) Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software 20 286–307.

See Also

logistf (package logistf) and brglm (package brglm) for alternative implementations of Firth's bias-reduced estimators.

Examples

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)

## Use firthglm.fit instead of glm.fit:
glm.D93 <- glm(counts ~ outcome + treatment, family = poisson(),
               method="firthglm.fit")
summary(glm.D93)