A – Optimal Design for Poisson Regression Model Using Square Root Link

N Swetha; Joshua David

doi:10.17485/IJST/v16i39.1999

Article

A – Optimal Design for Poisson Regression Model Using Square Root Link

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i39.1999

Year: 2023, Volume: 16, Issue: 39, Pages: 3407-3413

Original Article

A – Optimal Design for Poisson Regression Model Using Square Root Link

N Swetha^1*, Joshua David²

¹Research Scholar, Department of Statistics, Madras Christian College, Chennai, 600059, Tamil Nadu, India
²Assistant Professor, Department of Statistics, Madras Christian College, Chennai, 600059, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:07 August 2023, Accepted Date:13 September 2023, Published Date:25 October 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: The main objective of this study is to identify the optimal operating conditions by determining the point of least variation on response variables, crucial for various aspects of product quality such as yield or strength. Method: Newton-Raphson method is used and the solution to these formulas are obtained numerically using R-software. The parameters in the context of A-optimal designs is a necessary step i.e., θ= (α, β, μ). Findings: Our findings show that A-optimal designs outperform conventional design criteria in terms of lowering parameter estimate variance. Moreover, we illustrate how the A-optimal designs can lead to a more efficient allocation of resources statistical models, optimizing the use of time and resources while ensuring robust statistical conclusions. Novelty and Applications : In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focused on optimal experimental designs with concentration on D optimality. In this research, Poisson regression models were considered for A-optimization with square root link. This approach proves to be particularly valuable as it accounts for the model's dependence on unknown parameters, making it a useful technique for practical applications. Suggestions: This methodology is quite general and may be applied to find A-optimal designs for other models, like the Compound Poisson, Gamma and inverse Gaussian model, with log link or other types of optimal designs.

Keywords: AOptimality, Poisson Regression Model, Square Root Link, Experimental Design, Parameter Estimation

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Copyright

© 2023 Swetha & David. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)