The 'gfilogisreg' package

In gfilogisreg: Generalized Fiducial Inference for Binary Logistic Regression Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

The main function of the 'gfilogisreg' package is gfilogisreg. It simulates the fiducial distribution of the parameters of a logistic regression model.

To illustrate it, we will consider a logistic dose-response model for inference on the median lethal dose. The median lethal dose (LD50) is the amount of a substance, such as a drug, that is expected to kill half of its users.

The results of LD50 experiments can be modeled using the relation $$ \textrm{logit}(p_i) = \beta_1(x_i - \mu) $$ where $p_i$ is the probability of death at the dose administration $x_i$, and $\mu$ is the median lethal dose, i.e. the dosage at which the probability of death is $0.5$. The $x_i$ are known while $\beta_1$ and $\mu$ are fixed effects that are unknown.

This relation can be written in the form $$ \textrm{logit}(p_i) = \beta_0 + \beta_1 x_i $$ with $\mu = -\beta_0 / \beta_1$.

We will perform the fiducial inference in this model with the following data:

dat <- data.frame(
  x = c(
    -2, -2, -2, -2, -2, 
    -1, -1, -1, -1, -1, 
     0,  0,  0,  0,  0,
     1,  1,  1,  1,  1,
     2,  2,  2,  2,  2
  ),
  y = c(
    1, 0, 0, 0, 0,
    1, 1, 1, 0, 0,
    1, 1, 0, 0, 0,
    1, 1, 1, 1, 0,
    1, 1, 1, 1, 1
  )
)

Let's go:

library(gfilogisreg)
set.seed(666L)
fidsamples <- gfilogisreg(y ~ x, data = dat, N = 500L)

Here are the fiducial estimates and $95\%$-confidence intervals of the parameters $\beta_0$ and $\beta_1$:

gfiSummary(fidsamples)

The fiducial estimates are close to the maximum likelihood estimates:

glm(y ~ x, data = dat, family = binomial())

Now let us draw the fiducial $95\%$-confidence interval about our parameter of interest $\mu$:

gfiConfInt(~ -`(Intercept)`/x, fidsamples)

gfilogisreg documentation built on Dec. 21, 2021, 5:06 p.m.