Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917211755511808 |
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| author | Bhuyan, Prajamitra Halder, Soutik Jha, Jayant |
| author_facet | Bhuyan, Prajamitra Halder, Soutik Jha, Jayant |
| contents | This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various circular-circular and circular-linear regression models have been studied and applied to different real-world problems. However, there are no models for addressing zero-inflated circular observations in the context of longitudinal studies. Motivated by a real case study, a mixed-effects two-stage model based on the projected normal distribution is proposed to handle such issues. The interpretation of the model parameters is discussed and identifiability conditions are derived. A Bayesian methodology based on Gibbs sampling technique is developed for estimating the associated model parameters. Simulation results show that the proposed method outperforms its competitors in various situations. A real dataset on post-operative astigmatism is analyzed to demonstrate the practical implementation of the proposed methodology. The use of the proposed method facilitates effective decision-making for treatment choices and in the follow-up phases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13998 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology Bhuyan, Prajamitra Halder, Soutik Jha, Jayant Methodology Applications Computation This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various circular-circular and circular-linear regression models have been studied and applied to different real-world problems. However, there are no models for addressing zero-inflated circular observations in the context of longitudinal studies. Motivated by a real case study, a mixed-effects two-stage model based on the projected normal distribution is proposed to handle such issues. The interpretation of the model parameters is discussed and identifiability conditions are derived. A Bayesian methodology based on Gibbs sampling technique is developed for estimating the associated model parameters. Simulation results show that the proposed method outperforms its competitors in various situations. A real dataset on post-operative astigmatism is analyzed to demonstrate the practical implementation of the proposed methodology. The use of the proposed method facilitates effective decision-making for treatment choices and in the follow-up phases. |
| title | Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology |
| topic | Methodology Applications Computation |
| url | https://arxiv.org/abs/2601.13998 |