- Title
- The development of correspondence analysis techniques using the family of Cressie–Read power divergence statistics
- Creator
- Alzahrani, Asma Ahmad
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2024
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Correspondence analysis (CA) is a visual statistical technique that has a long and interesting history. It is a powerful multivariate statistical technique that aims to uncover underlying patterns and associations between two or more categorical variables. As datasets continue to expand in complexity and size, there is a growing need for advanced analytical techniques that can handle and extract meaningful insights from such data. The classical approach to CA considers Pearson’s chi-squared statistic as the fundamental measure of association between categorical variables. However, this thesis provides an extension to CA techniques by employing the family of Cressie-Read divergence statistics as a measure to examine the association between the categorical variables. This family includes the most common statistics of association such as Pearson’s statistic, the Freeman-Tukey statistic, the log-likelihood ratio statistic, and the Cressie-Read statistic. Thus, by using the family of Cressie-Read divergence statistics to conduct CA, a more comprehensive understanding can be obtained, which expands the analysis beyond Pearson’s statistic. This thesis describes this approach to CA in detail and highlights its features by providing various applications. Moreover, we further generalise the approach to enable the analysis of multiple categorical variables. A new technique for constructing confidence regions based on the family of Cressie-Read divergence statistics is also explored. Further extensions of this area of CA are also made by showing how it can be used to analyse the association between the variables of a multi-way contingency table. The results of such analyses allow for a highly effective visual exploration of the association structure between categorical variables. Additionally, R functions for all techniques discussed in the thesis are provided. This, in turn, provides a significant contribution for researchers wanting to increase their flexibility in programming and create new and powerful tools for categorical data analysis.
- Subject
- correspondence analysis; visual statistical technique; Cressie-Read family; divergence statistics
- Identifier
- http://hdl.handle.net/1959.13/1510659
- Identifier
- uon:56438
- Rights
- Copyright 2024 Asma Ahmad Alzahrani
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 3 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 231 KB | Adobe Acrobat PDF | View Details Download |