Chinwan, Amit
(2024)
Visualising Bivariate Patterns using
Association Measures.
PhD thesis, National University of Ireland Maynooth.
Abstract
Correlation matrix displays are valuable tools for investigating bivariate associations,
typically showcasing Pearson’s correlation—a linear association measure—for
pairs of numerical variables. However, these displays have limitations in capturing
complex non-linear associations and associations involving categorical variables.
This thesis addresses these limitations by introducing alternative association measures
that accommodate pairs of numerical, ordinal, and categorical variables, as
well as mixed pairs where one variable is categorical and the other is numerical. For
numerical variables, we incorporate modern non-linear association measures like
distance correlation and the maximal information coefficient (MIC). Notably, our
displays present multiple association measures for each variable pair, revealing patterns
beyond linear associations or associations dependent on levels of a grouping
variable. To address space issues with high-dimensional datasets, we also offer a linear
layout display, showing one or more association measures for each variable pair.
Furthermore, we employ seriation for matrix displays and importance sorting for
linear displays to emphasize highly-associated variables or pairs with significant differences,
making them easier to discern and interpret. These improvements enhance
the effectiveness and efficiency of data analysis, allowing for a more comprehensive
understanding of associations in various datasets.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Visualising; Bivariate Patterns;
Association Measures; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: |
18317 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
26 Mar 2024 13:53 |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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