Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya

Paul Mwangi Kariuki; James Mwangi Kahiri

doi:doi:10.11648/j.ajtas.20251405.11

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Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya

Paul Mwangi Kariuki

, James Mwangi Kahiri^*

Published in American Journal of Theoretical and Applied Statistics (Volume 14, Issue 5)

Received: 30 August 2025 Accepted: 10 September 2025 Published: 26 September 2025

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Abstract

The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.

Published in	American Journal of Theoretical and Applied Statistics (Volume 14, Issue 5)
DOI	10.11648/j.ajtas.20251405.11
Page(s)	203-210
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Multinomial Regression, Newton-Raphson Method, Fisher’s Scoring Method, Reweighted Least Squares Method, Childhood Malnutrition, Evidence-based Decision-making, Public Health Interventions

References

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[2]	Long, J. S. (2012). Regression models for nominal and ordinal outcomes. In J. Best & W. Wolf (Eds.), Regression models (pp. 45-73). Thousand Oaks, CA: Sage Publications. https://doi.org/10.4135/9781446288146.n9
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[4]	Etim, K. D. (2016). Nutritional status of children under five years in Ekureku community, Abi L. G. A. of Cross River State, Nigeria (Master’s thesis, University of Calabar, Nigeria). https://doi.org/10.7537/marsnys130320.07
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[7]	Getacher, L., Ademe, B. W., & Belachew, T. (2023). Double burden of malnutrition and its associated factors among adolescents in Debre Berhan Regiopolitan City, Ethiopia: a multinomial regression model analysis. Frontiers in Nutrition, 10, 1187875. https://doi.org/10.3389/fnut.2023.1187875
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[12]	Katoch, O. R. (2022). Determinants of malnutrition among children: A systematic review. Nutrition, 96, 111565. https://doi.org/10.1016/j.nut.2021.111565
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[14]	Agho, K. E., Akombi, B. J., Ferdous, A. J., Mbugua, I., & Kamara, J. K. (2019). Childhood undernutrition in three disadvantaged East African Districts: a multinomial analysis. BMC Pediatrics, 19, 118. https://doi.org/10.1186/s12887-019-1482-y
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APA Style

Kariuki, P. M., Kahiri, J. M. (2025). Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. American Journal of Theoretical and Applied Statistics, 14(5), 203-210. https://doi.org/10.11648/j.ajtas.20251405.11

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ACS Style

Kariuki, P. M.; Kahiri, J. M. Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. Am. J. Theor. Appl. Stat. 2025, 14(5), 203-210. doi: 10.11648/j.ajtas.20251405.11

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AMA Style

Kariuki PM, Kahiri JM. Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. Am J Theor Appl Stat. 2025;14(5):203-210. doi: 10.11648/j.ajtas.20251405.11

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@article{10.11648/j.ajtas.20251405.11,
  author = {Paul Mwangi Kariuki and James Mwangi Kahiri},
  title = {Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {5},
  pages = {203-210},
  doi = {10.11648/j.ajtas.20251405.11},
  url = {https://doi.org/10.11648/j.ajtas.20251405.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251405.11},
  abstract = {The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.
},
 year = {2025}
}

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TY  - JOUR
T1  - Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya

AU  - Paul Mwangi Kariuki
AU  - James Mwangi Kahiri
Y1  - 2025/09/26
PY  - 2025
N1  - https://doi.org/10.11648/j.ajtas.20251405.11
DO  - 10.11648/j.ajtas.20251405.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 203
EP  - 210
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20251405.11
AB  - The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.

VL  - 14
IS  - 5
ER  -

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Author Information

Paul Mwangi Kariuki

Department of Statistics and Actuarial Science, School of Pure and Applied Sciences, Kenyatta University, Nairobi, Kenya

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http://orcid.org/0009-0008-0154-4006
James Mwangi Kahiri

Department of Statistics and Actuarial Science, School of Pure and Applied Sciences, Kenyatta University, Nairobi, Kenya

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APA Style

Kariuki, P. M., Kahiri, J. M. (2025). Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. American Journal of Theoretical and Applied Statistics, 14(5), 203-210. https://doi.org/10.11648/j.ajtas.20251405.11

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ACS Style

Kariuki, P. M.; Kahiri, J. M. Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. Am. J. Theor. Appl. Stat. 2025, 14(5), 203-210. doi: 10.11648/j.ajtas.20251405.11

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AMA Style

Kariuki PM, Kahiri JM. Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya. Am J Theor Appl Stat. 2025;14(5):203-210. doi: 10.11648/j.ajtas.20251405.11

Copy | Download

@article{10.11648/j.ajtas.20251405.11,
  author = {Paul Mwangi Kariuki and James Mwangi Kahiri},
  title = {Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {5},
  pages = {203-210},
  doi = {10.11648/j.ajtas.20251405.11},
  url = {https://doi.org/10.11648/j.ajtas.20251405.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251405.11},
  abstract = {The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Application of Newton Raphson, Fisher’s Scoring, and Reweighted Least Squares Methods for Multinomial Regression in Investigating Childhood Malnutrition in Kenya

AU  - Paul Mwangi Kariuki
AU  - James Mwangi Kahiri
Y1  - 2025/09/26
PY  - 2025
N1  - https://doi.org/10.11648/j.ajtas.20251405.11
DO  - 10.11648/j.ajtas.20251405.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 203
EP  - 210
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20251405.11
AB  - The study of causality in multivariate relationships in scientific studies involves the application of stochastic models in quantifying complex relationships. Stochastic models are becoming increasingly significant in health research due to their adaptability in practical situations and their ability to capture randomness, assess uncertainty, and inform decision-making. The models also provide reliable performance in capturing the complex determinants of malnutrition, demonstrating prediction precision and explanatory power. This study applies iterative parameter estimation methods for the multinomial regression model to investigate factors influencing childhood malnutrition in Kenya. Using data from the 2022 Kenya Demographic and Health Survey (KDHS), the research applies Newton-Raphson, Fisher’s Scoring, and Reweighted Least Squares methods to estimate parameters of the model and assess their classification performance. The study evaluates classification accuracy, goodness of fit, computational time, and predictive power of each method to identify the most reliable approach for modeling multinomial outcomes of childhood malnutrition, including stunting, wasting, underweight, and overweight. The methodological novelty of this study is the systematic comparison of iterative estimation methods, and the practical implications of selecting a method consistent with study objectives. By revealing causal relationships between malnutrition outcomes and significant demographic, socioeconomic, and environmental factors, the study aims to improve the analysis of multinomial datasets, provide accurate estimates, and support evidence-based decision-making for public health interventions in Kenya. The study results therefore, demonstrate practical policy implications for interventions toward high-risk children, prioritizing resource allocation and ensuring stronger credibility of evidence that supports nutritional policy decisions.

VL  - 14
IS  - 5
ER  -

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