Combined Model Approach to the Problem of Ranking

Abstract

Ranking can be defined in many ways and has been applied in many areas. Over the past years, many research studies have been conducted on ranking methods for decision-making. The issue is that results pertaining to ranking entities are based only on one method, which can be subjective and prone to biases. As a result, results vary from method to method. To resolve this issue, a combined model approach is proposed, in which multiple methods are taken into account. The goals of the combined model are to rank entities more objectively and obtain more reliable results. The combined model has both qualitative and quantitative elements, where the qualitative element is the ranking and clustering, while the quantitative element is comprised of the scores. Since ranking is based on the scores of the entities, it takes into account the distribution of scores. In some scenarios, closely ranked entities can have similar scores, while in other scenarios, their scores can be relatively different even though they are ranked close to one another. The score distribution leads to clustering analysis, where entities are divided into clusters based on the spread of the scores. Hence, the combined model takes into account not only the ranks but also the scores of the entities. The proposed combined model is applied to three areas for this dissertation research. The first is identifying and ranking road hotspots and predicting the number of traffic crashes in road segments using the Empirical Bayesian (EB) enhanced by the Proportion Discordance Ratio (PDR) metric. The effectiveness of the Enhanced EB method is tested and demonstrated through a case study that is conducted in one of the major highways in Phoenix, Arizona. The second is ranking major US metropolitan areas in traffic congestion using unsupervised learning based on the Normalized Scoring Method (NSM), Principal Component Analysis (PCA), and the PDR similarity matrix. In 2015, TomTom ranked Tucson as the 21st most congested metropolitan area in the US, and the unsupervised learning combined model is applied to assess TomTom’s traffic congestion ranking of the metropolitan areas in order to determine if Tucson is highly congested based on the proposed model. The third is ranking and assessing the Hall of Fame (HOF) worthiness of retired Major League Baseball players based on their performance statistics through supervised learning based on Support Vector Machines (SVM) and Neural Networks (NN). Players are considered for the HOF through a voting procedure, where voters are comprised of members of the media, but there is a possibility of voting bias that can favor or go against certain players. Results from all three scenarios show that the proposed combined models are more reliable and can more objectively rank entities in order to correct biases based on previous methodologies.