logitexp: Logistic-exposure link function.

In trobinj/trtools: Miscellaneous Tools for Teaching Statistics

Logistic-exposure link function.

Description

This is a link function proposed by Schaffer (2004) for discrete time survival modeling. Let T be the number of discrete time units until an event (e.g., days), and assume that for a given unit the hazard function P(T > t | T \ge t) = \pi for all t (i.e., the probability of surviving time unit t is \pi). Then the probability of survived e time units is \pi^e. Assume a logistic regression model for survival on a given day so that \pi = 1/(1 + exp(-\eta)). Let Y be the number of observational units out of m that survive an exposure of e time units. Then the inverse link function is E(Y/m) = 1/(1 + exp(-\eta))^e, and the link function is [\log(E(Y/m)^{1/e}/(1 - E(Y/m)^{1/e})] = \eta.

Usage

logitexp(exposure = 1)

Details

The argument exposure specifies the number of time units. To be consistent with the motivation given above this should be a positive integer.

Note

The code for this link function is also given as an example in the documentation for family.

Source

Schaffer, T. L. (2004). A unified approach to analyzing nest success. The Auk, 121(2), 526-540.

See Also

logitcomp

Examples

library(dplyr)

set.seed(123)

d <- data.frame(x = seq(0, 3, length = 100)) %>%
 mutate(days = sample(1:10, n(), replace = TRUE)) %>% 
 mutate(y = rbinom(n(), 1, plogis(x)^days))

m <- glm(y ~ x, data = d, 
 family = binomial(link = logitexp(exposure = d$days)))
 
# The logitcomp link function can be used to model the probability
# of not surviving. The following produces the same estimates except
# for a reversal of sign. 

m <- glm(1 - y ~ x, data = d, 
 family = binomial(link = logitcomp(m = d$days)))

trobinj/trtools documentation built on Jan. 28, 2024, 3:20 a.m.