Multinomial goodness-of-fit tests for logistic regression models

Area of Science:

• Statistics
• Biostatistics
• Medical Informatics

Background:

• Assessing model fit is crucial for multinomial logistic regression.
• Existing goodness-of-fit tests may have limitations in certain scenarios.

Purpose of the Study:

• To evaluate the performance of a new goodness-of-fit test, Cg, for multinomial logistic regression.
• To compare the Cg test with the Pearson chi2 (X2) and normalized (z) tests.

Main Methods:

• A novel test (Cg) was developed by sorting observations and creating a g x c contingency table.
• Pearson chi2 and normalized tests (X2, z) were used for comparison.
• Monte Carlo simulations were conducted to assess null distributions and power.

Main Results:

• The Cg test's null distribution is well-approximated by the chi2 distribution.
• The Cg test demonstrated low power with small sample sizes (n=100) but satisfactory power with larger samples (n=400).
• The X2 test showed erratic behavior, while the z test generally adhered to the standard normal distribution.

Conclusions:

• The Cg test is a viable goodness-of-fit measure for multinomial logistic regression, particularly with adequate sample sizes.
• The Cg test offers an alternative to traditional methods, with performance improving as sample size increases.
• The study highlights the importance of sample size in evaluating goodness-of-fit tests for complex regression models.