separation.detection {brglm}

Separation Identification.

Description

Provides a tool for identifying whether or not separation has occurred.

Usage

separation.detection(fit, nsteps = 30)

Arguments

fit

the result of a glm call.

nsteps

Starting from maxit = 1, the GLM is refitted for maxit = 2, maxit = 3, ..., maxit = nsteps. Default value is 30.

Details

Identifies separated cases for binomial-response GLMs, by refitting the model. At each iteration the maximum number of allowed IWLS iterations is fixed starting from 1 to nsteps (by setting control = glm.control(maxit = j), where j takes values 1, ..., nsteps in glm). For each value of maxit, the estimated asymptotic standard errors are divided to the corresponding ones resulted for control = glm.control(maxit = 1). Based on the results in Lesaffre & Albert (1989), if the sequence of ratios in any column of the resulting matrix diverges, then separation occurs and the maximum likelihood estimate for the corresponding parameter has value minus or plus infinity.

Value

A matrix of dimension nsteps by length(coef(fit)), that contains the ratios of the estimated asymptotic standard errors.

Author(s)

Ioannis Kosmidis, [e-mail]

References

Kosmidis I. and Firth D. (2021). Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. Biometrika, 108, 71–82.

Lesaffre, E. and Albert, A. (1989). Partial separation in logistic discrimination. J. R. Statist. Soc. B, 51, 109–116.

Examples

## Begin Example
y <- c(1,1,0,0)
totals <- c(2,2,2,2)
x1 <- c(1,0,1,0)
x2 <- c(1,1,0,0)
m1 <- glm(y/totals ~ x1 + x2, weights = totals, family = binomial())
# No warning from glm...
m1
# However estimates for (Intercept) and x2 are unusually large in
# absolute value... Investigate further:
#
separation.detection(m1,nsteps=30)
# Note that the values in the column for (Intercept) and x2 diverge,
# while for x1 converged. Hence, separation has occurred and the
# maximum lieklihood estimate for (Intercept) is minus infinity and
# for x2 is plus infinity. The signs for infinity are taken from the
# signs of (Intercept) and x1 in coef(m1).
## End Example