glm_grouped {parsnip}

Fit a grouped binomial outcome from a data set with case weights

Description

stats::glm() assumes that a tabular data set with case weights corresponds to "different observations have different dispersions" (see ?glm).

In some cases, the case weights reflect that the same covariate pattern was observed multiple times (i.e., frequency weights). In this case, stats::glm() expects the data to be formatted as the number of events for each factor level so that the outcome can be given to the formula as cbind(events_1, events_2).

glm_grouped() converts data with integer case weights to the expected "number of events" format for binomial data.

Usage

glm_grouped(formula, data, weights, ...)

Arguments

formula

A formula object with one outcome that is a two-level factors.

data

A data frame with the outcomes and predictors (but not case weights).

weights

An integer vector of weights whose length is the same as the number of rows in data. If it is a non-integer numeric, it will be converted to integer (with a warning).

...

Options to pass to stats::glm(). If family is not set, it will automatically be assigned the basic binomial family.

Value

A object produced by stats::glm().

Examples

#----------------------------------------------------------------------------
# The same data set formatted three ways

# First with basic case weights that, from ?glm, are used inappropriately.
ucb_weighted <- as.data.frame(UCBAdmissions)
ucb_weighted$Freq <- as.integer(ucb_weighted$Freq)
head(ucb_weighted)
nrow(ucb_weighted)

# Format when yes/no data are in individual rows (probably still inappropriate)
library(tidyr)
ucb_long <- uncount(ucb_weighted, Freq)
head(ucb_long)
nrow(ucb_long)

# Format where the outcome is formatted as number of events
ucb_events <-
  ucb_weighted %>%
  tidyr::pivot_wider(
    id_cols = c(Gender, Dept),
    names_from = Admit,
    values_from = Freq,
    values_fill = 0L
  )
head(ucb_events)
nrow(ucb_events)

#----------------------------------------------------------------------------
# Different model fits

# Treat data as separate Bernoulli data:
glm(Admit ~ Gender + Dept, data = ucb_long, family = binomial)

# Weights produce the same statistics
glm(
  Admit ~ Gender + Dept,
  data = ucb_weighted,
  family = binomial,
  weights = ucb_weighted$Freq
)

# Data as binomial "x events out of n trials" format. Note that, to get the same
# coefficients, the order of the levels must be reversed.
glm(
  cbind(Rejected, Admitted) ~ Gender + Dept,
  data = ucb_events,
  family = binomial
)

# The new function that starts with frequency weights and gets the correct place:
glm_grouped(Admit ~ Gender + Dept, data = ucb_weighted, weights = ucb_weighted$Freq)