Introduction: A typical task in quantitative data analysis is to derive estimates of population parameters based on sample statistics. For manifest variables this is usually a straightforward process utilising suitable measurement instruments and standard statistics such the mean, median and standard deviation. Latent variables on the other hand are typically more elusive, making it difficult to obtain valid and reliable measurements. One of the most widely used methods of estimating the parameter value of a latent variable is to use a summated score derived from a set of individual scores for each of the various attributes of the latent variable. A serious limitation of this method and other similar methods is that the validity and reliability of measurements depend on whether the statements included in the questionnaire cover all characteristics of the variable being measured and also on respondents’ ability to correctly indicate their perceived assessment of the characteristics on the scale provided. Methods without this limitation and that are especially useful where a set of objects/entities must be ranked based on the parameter values of one or more latent variables, are methods of paired comparisons. Although the underlying assumptions and algorithms of these methods often differ dramatically, they all rely on data derived from a series of comparisons, each consisting of a pair of specimens selected from the set of objects/entities being investigated. Typical examples of the comparison process are: subjects (judges) who have to indicate for each pair of objects which of the two they prefer; sport teams that compete against each other in matches that involve two teams at a time. The resultant data of each comparison range from a simple dichotomy to indicate which of the two objects are preferred/better, to an interval or ratio scale score for e d Bradley-Terry models, and were based on statistical theory assuming that the variable(s) being measured is either normally (Thurstone-Mosteller) or exponentially (Bradley-Terry) distributed. For many years researchers had to rely on these PCM’s when analysing paired comparison data without any idea about the implications if the distribution of the data from which their sample were obtained differed from the assumed distribution for the applicable PCM being utilised. To address this problem, PCM’s were subsequently developed to cater for discrete variables and variables with distributions that are neither normal or exponential. A question that remained unanswered is how the performance, as measured by the accuracy of parameter estimates, of PCM's are affected if they are applied to data from a range of discrete and continuous distribution that violates the assumptions on which the applicable paired comparison algorithm is based. This study is an attempt to answer this question by applying the most popular PCM's to a range of randomly derived data sets that spans typical continuous and discrete data distributions. It is hoped that the results of this study will assist researchers when selecting the most appropriate PCM to obtain accurate estimates of the parameters of the variables in their data sets.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nmmu/vital:11087 |
| Date | January 2004 |
| Creators | Venter, Daniel Jacobus Lodewyk |
| Publisher | University of Port Elizabeth, Faculty of Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Masters, MSc |
| Format | 138 pages, pdf |
| Rights | Nelson Mandela Metropolitan University |
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