Model-based goodness-of-fit tests for the ordered stereotype model

Area of Science:

• Statistics
• Biostatistics
• Ordinal Regression Analysis

Background:

• Ordinal response variables are common in many scientific fields.
• The ordered stereotype model offers flexibility in modeling ordinal data by allowing uneven category spacing.
• Existing goodness-of-fit tests may not fully capture the nuances of this model.

Purpose of the Study:

• To develop and present two new model-based goodness-of-fit tests for the ordered stereotype model.
• To adapt the Lipsitz test methodology for assessing the fit of ordered stereotype models.
• To evaluate the performance of the proposed tests across various data scenarios.

Main Methods:

• The proposed tests are based on the Lipsitz test, partitioning subjects into G groups.
• An alternative model is constructed by adding group effects to the null model.
• Two variations of the test are presented: one using the ordered stereotype model structure and another using an ordinary linear model.
• The tests leverage the data-driven uneven spacing of ordinal response categories inherent to the ordered stereotype model.

Main Results:

• The performance of the two new goodness-of-fit tests was demonstrated under diverse simulated scenarios.
• The application of the tests in three real-world examples was presented.
• The study provides enhanced tools for validating the ordered stereotype model in statistical analyses.

Conclusions:

• The developed goodness-of-fit tests offer a valuable addition to the statistical toolkit for analyzing ordinal data.
• These tests provide a robust method for assessing the fit of the ordered stereotype model, considering its unique feature of data-driven category spacing.
• The findings support the utility of these tests in various applied research settings involving ordinal outcomes.