Are all Linear Paired Comparison Models Equivalent
Abstract
Previous authors have found that different models of paired comparisons data lead to similar fits. This phenomenon is examined by means of a set of paired comparison models, based on gamma random variables, that includes the frequently applied Bradley-Terry and Thurstone-Mosteller models. A theoretical result provides a natural ordering of the models in the gamma family on the basis of their composition rules. Analysis of several sports data sets indicates that all of the paired comparison models in the family provide adequate, and almost identical, fits to the data. Simulations are used to further explore this result. Although not all approaches to paired comparisons experiments are covered by this discussion, the evidence is strong that for samples of the size usually encountered in practice all linear paired comparison models are virtually equivalent.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1990
- Accession Number
- ADA236856
Entities
People
- Hal Stern
Organizations
- Harvard University