The method of paired comparisons is seen as a technique used to rank a set of objects with respect to an abstract or immeasurable property. To do this, the objects get to be compared two at a time. The results are input into a model, resulting in numbers known as weights being assigned to the objects. The weights are then used to rank the objects. The method of paired comparisons was first used for psychometric investigations. Various other applications of the method are also present, for example economic applications, and applications in sports statistics. This study involves taking paired comparison models and making them time-dependent. Not much research has been done in this area. Three new time series models for paired comparisons are created. Simulations are done to support the evidence obtained, and theoretical as well as practical examples are given to illustrate the results and to verify the efficiency of the new models. A literature study is given on the method of paired comparisons, as well as on the areas in which we apply our models. Our first two time series models for paired comparisons are the Linear-Trend Bradley- Terry Model and the Sinusoidal Bradley-Terry Model. We use the maximum likelihood approach to solve these models. We test our models using exact and randomly simulated data for various time periods and various numbers of objects. We adapt the Linear-Trend Bradley-Terry Model and received our third time series model for paired comparisons, the Log Linear-Trend Bradley-Terry Model. The daily maximum and minimum temperatures were received for Port Elizabeth, Uitenhage and Coega for 2005 until 2009. To evaluate the performance of the Linear-Trend Bradley-Terry Model and the Sinusoidal Bradley-Terry Model on estimating missing temperature data, we artificially remove observations of temperature from Coega’s temperature dataset for 2006 until 2008, and use various forms of these models to estimate the missing data points. The exchange rates for 2005 until 2008 between the following currencies: the Rand, Dollar, Euro, Pound and Yen, were obtained and various forms of our Log Linear-Trend Bradley-Terry Model are used to forecast the exchange rate for one day ahead for each month in 2006 until 2008. One of the features of this study is that we apply our time series models for paired comparisons to areas which comprise non-standard paired comparisons; and we want to encourage the use of the method of paired comparisons in a broader sense than what it is traditionally used for. The results of this study can be used in various other areas, like for example, in sports statistics, to rank the strength of sports players and predict their future scores; in Physics, to calculate weather risks of electricity generation, particularly risks related to nuclear power plants, and so forth, as well as in many other areas. It is hoped that this research will open the door to much more research in combining time series analysis with the method of paired comparisons.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nmmu/vital:10577 |
| Date | January 2011 |
| Creators | Sjolander, Morne Rowan |
| Publisher | Nelson Mandela Metropolitan University, Faculty of Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Doctoral, PhD |
| Format | 361 leaves, pdf |
| Rights | Nelson Mandela Metropolitan University |
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