The number of response categories in ordered response models

Area of Science:

• Statistics
• Biostatistics
• Psychometrics

Background:

• Categorizing continuous responses is common in research.
• The number of response categories (m) significantly influences data analysis outcomes.
• Proportional Odds Models offer a method to analyze ordinal data with varying category numbers.

Purpose of the Study:

• To investigate the impact of the number of response categories (m) on statistical analysis.
• To evaluate the asymptotic efficiency of regression coefficient estimators and inferential procedures.
• To determine the optimal number of categories for different sample sizes.

Main Methods:

• Utilized Proportional Odds Models with closed-form information matrices.
• Analytically evaluated asymptotic efficiency without simulations.
• Investigated the effects of category merging and dichotomization on estimator efficiency.

Main Results:

• Finer categorization (larger m) augments data information content.
• Asymptotic efficiency and statistical test power increase with the number of categories (m).
• Category merging, especially dichotomization, leads to significant information loss and reduced efficiency.

Conclusions:

• A higher number of response categories generally leads to more accurate and powerful statistical analyses.
• The choice of m should consider sample size, with more categories potentially compensating for smaller samples.
• Careful consideration of category merging is crucial to avoid detrimental information loss.