A Mathematical Model for a Paired Comparison Experiment on a Continuum of Response.
Abstract
This research uses a Bradley-Terry paired comparison model, extending the possible outcomes from a simple binary response to any point along a continuum. An integrated mean squared error approach is used as a basis for parameter estimation based on an underlying logistic model and for estimating a function that maps a response from the real line onto the interval (0,1). Evaluation of the parameter estimates is performed using an underlying logistic sampling distribution with a logistic mapping function. The asymptotic behavior of the estimates involves the use of linear combinations of order statistics, also called L-statistics. Using this approach it is shown that the parameter estimates are consistent but slightly biased. A simulation study with randomly generated values from a standard logistic distribution were used for response values in a paired comparison experiment. Samples for 3, 4, and 5 treatments with 5, 10, 25, and at times 50, replications for each pairing were considered. The values for the parameter estimates for these samples are presented along with the graphs of the estimated inverse mapping function. Density smoothing techniques using a kernel estimator were employed to further explore the shape of the derivative of the inverse mapping function. This continuous model was then reformulated into a Likert scale with five possible responses from any comparison. An ad hoc method and weighed least squares were used to determine the discriminating values for the Likert scale.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1990
- Accession Number
- ADA239858
Entities
People
- Kaye A. De Ruiz
Organizations
- Air Force Institute of Technology