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Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution
Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613564455354368 |
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| access_status_str | Open Access |
| author2 | Burger, Divan A. |
| author_browse | Burger, Divan A. |
| author_facet | Burger, Divan A. |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/78073 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:08.659Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/78073 Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution Burger, Divan A. nlientjie@gmail.com Nel, Helene Mari UCTD Mathematical statistics 895 (WST 895) Mini Dissertation (MSc (Advanced Data Analytics))--University of Pretoria, 2021. Longitudinal data refer to multiple observations collected on the same subject (or unit) over time. Zero-inflated data (containing many zeros) frequently occur, resulting in overdispersion in count data. Regression models used to analyze count data are often based on the Poisson and negative binomial (NB) distribution. The Poisson distribution is restrictive when count data are overdispersed; the regression model can, therefore, give inappropriate fits when the variability in the data is larger or smaller than the theoretical variance. These two cases are, respectively, referred to as overdispersion and underdispersion. The NB distribution handles overdispersed data better compared to the Poisson distribution, but not underdispersed data. Another problem with the NB distribution is that it does not accommodate heavy-tailed or highly skewed data well. In this study, the discrete Weibull (DW) and the zero-inflated DW (ZIDW) distributions are explored in a mixed model context that models the median using a Bayesian approach. In contrast, the conventional NB and ZINB mixed-effects regression models model the mean counts over time. Results from the four mixed-effects regression models are compared. It is observed that the Bayesian DW and ZIDW mixed-effects regression models are computationally competitive with the Bayesian NB and ZINB mixed-effects regression models concerning flexibility, implementation, and convergence speed. The DW and ZIDW models are found to be excellent choices to model highly skewed longitudinal count data. NRF Statistics MSc (Advanced Data Analytics) Unrestricted 2021-01-21T08:13:59Z 2021-01-21T08:13:59Z 2021 2021 Mini Dissertation * A2021 http://hdl.handle.net/2263/78073 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Mathematical statistics 895 (WST 895) Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title | Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title_full | Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title_fullStr | Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title_full_unstemmed | Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title_short | Modelling of highly skewed longitudinal count data based on the discrete Weibull distribution |
| title_sort | modelling of highly skewed longitudinal count data based on the discrete weibull distribution |
| topic | UCTD Mathematical statistics 895 (WST 895) |
| url | http://hdl.handle.net/2263/78073 |