CLRtools (version 0.1.0)

osius_rojek: Osius and Rojek Goodness-of-Fit Test for Logistic Regression

Description

Applies the Osius and Rojek normal approximation to assess the overall goodness-of-fit of a logistic regression model. This includes:

• A normal approximation to the distribution of the Pearson chi-square statistic.

• A normal approximation to the distribution of the sum-of-squares statistic.

Usage

osius_rojek(model)

Value

A list containing the following measures:

z_chisq

The standardized Z-statistic based on the Pearson chi-square approximation.

p_value

The two-sided p-value associated with z_chisq.

z_s

The standardized Z-statistic based on the sum-of-squares approximation.

p_value_S

The two-sided p-value associated with z_s.

Arguments

model

A logistic regression model fitted with glm().

Details

This function implements the Osius and Rojek test as described in Hosmer et al. (2013) for assessing the goodness-of-fit of logistic regression models.

References

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression (3rd ed.). John Wiley & Sons, Inc.

See Also

cov.patterns

Examples

# Example from Hosmer et al., 2013
# Applied Logistic Regression (3rd ed.), Chapter 5, Section 5.2.2

# Recode 'raterisk' into a binary variable 'raterisk_cat'
glow500 <- dplyr::mutate(
  glow500,
  raterisk_cat = dplyr::case_when(
    raterisk %in% c("Less", "Same") ~ "C1",
    raterisk == "Greater" ~ "C2"
  )
)

# Fit a multiple logistic regression model with interactions
model.int <- glm(
  fracture ~ age + height + priorfrac + momfrac + armassist +
    raterisk_cat + age * priorfrac + momfrac * armassist,
  family = binomial,
  data = glow500
)

# Apply the Osius and Rojek test for goodness-of-fit
osius_rojek(model.int)