A goodness-of-fit test for multinomial logistic regression

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Logistic regression is widely used for modeling categorical outcomes.
• Assessing the goodness-of-fit for logistic regression models, especially with multiple categories, remains a challenge.
• Existing methods may lack the flexibility to detect specific types of model misspecification.

Purpose of the Study:

• To develop a novel score test for evaluating the fit of logistic regression models with two or more outcome categories.
• To provide a flexible framework for testing goodness-of-fit against specific alternatives.
• To interpret the proposed test statistic within the context of random effects models.

Main Methods:

• A score test statistic is proposed, based on a sum of squared smoothed residuals.
• The test statistic is derived by considering a random effects model formulation.
• The distance metric in covariate space is specified by the user to define the alternative hypothesis.

Main Results:

• The proposed statistic is shown to be a score test under a random effects model.
• The test allows users to tailor the alternative hypothesis by selecting a distance metric.
• This enables the test to function as an omnibus goodness-of-fit test or a specific test for lack of fit.

Conclusions:

• The developed score test offers a flexible and powerful tool for assessing logistic regression model fit with multiple outcome categories.
• The ability to specify the distance metric enhances the test's utility for detecting various forms of model misspecification.
• This approach contributes to more robust statistical modeling in fields utilizing logistic regression.