CLRtools (version 0.1.0)

residuals_logistic: Model Diagnostic for Logistic Regression Models

Description

This function computes various residuals and diagnostic measures for logistic regression models, including Pearson residuals, standardized Pearson residuals, deviance residuals, leverage, and delta statistics (change in Pearson chi-squared, change in deviance, and change in Cook's distance). The function also generates diagnostic plots for evaluating the model fit and identifying influential data points.

Usage

residuals_logistic(model)

Value

A list containing:

x.cv

A data frame with the computed residuals and diagnostic measures for each observation, and their respective covariates.

leverage

A ggplot object displaying leverage vs. estimated probability.

change.Pearsonchi

A ggplot object displaying the change in Pearson chi-squared vs. estimated probability.

change.deviance

A ggplot object displaying the change in deviance vs. estimated probability.

cooks

A ggplot object displaying Cook's distance vs. estimated probability.

change.Pb

A ggplot object displaying the change in Pearson chi-squared vs. Estimated Probability with size determinate by Cook's distance.

Arguments

model

A fitted logistic regression model of class glm.

Details

The residuals and diagnostic measures are computed using standard formulas for logistic regression (adapted from Hosmer et al., 2013, Applied Logistic Regression, 3rd ed.). The following measures are computed:

• Pearson residuals

• Standardized Pearson residuals

• Deviance residuals

• Leverage

• Delta statistics: Delta beta (change in Cook's distance), Delta chi (change in Pearson chi-squared) and Delta deviance

Additionally, the function generates the following plots:

• Leverage vs. Estimated Probability

• Change in Pearson chi-squared vs. Estimated Probability

• Change in Deviance vs. Estimated Probability

• Cook's Distance vs. Estimated Probability

• Change in Pearson chi-squared vs. Estimated Probability

• Change in Pearson chi-squared vs. Estimated Probability with size determinate by Cook's distance.

References

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression (3rd ed.). John Wiley & Sons, Inc. The formulas for calculating residuals and diagnostics are adapted from this source.

See Also

cov.patterns

Examples

# Example from Hosmer et al., 2013
# Applied Logistic Regression (3rd ed.), Chapter 5, Section 5.3

# 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
)

# Run diagnostics for the logistic model
residuals_logistic(model.int)