American Journal of Theoretical and Applied Statistics

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Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya

Received: 05 October 2020    Accepted: 19 October 2020    Published: 26 October 2020
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Abstract

Serious violent crimes including Burglary, dangerous drug trafficking and sexual offenses make up the bulk of incidents filed at police stations daily. These crimes related activities poses a serious threat to the peace and serenity of a nation as far as safety is concerned. Burglar incidents data are often discrete and do not conform to the general assumptions of the linear model and its variants. Ordinarily, such data could be modeled using a linear regression approach to derive the relationship between the response variable to the underlying covariates. However, the narrowing of the gap between city and suburban burglar crime rates brings about variability invalidating the application of Ordinary linear regression approaches. The main objective of this study focused on the comparative use of Generalized Poisson and Quasi-Poisson models as an alternative to the classical linear regression approach in modeling Burglar incidents in Nairobi City County, Kenya. The prime advantage of applying Quasi Poisson in count data analysis is that it fixes the basic fallacy of assuming homogeneity in data and allows estimation of dispersion. The study used secondary data covering Eight (8) Nairobi's Administrative Divisions from the National Crime Research Center (NCRC) for the period 2016-2018. The comparison criteria were the Akaike Information (AIC) Criterion and Deviance Information Criterion (DIC) alongside other model diagnostics tests. Application of this results in burglar events revealed that the number of incidents in the study area are Under-dispersed with the risks of experiencing Burglar crime being above 5% in all the locations surveyed. In an attempt to explore Burglar to location relationship, results from study proved that Generalized Poisson Model performed better than the Quasi Poisson model having posted the lowest AIC value.

DOI 10.11648/j.ajtas.20200905.19
Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5, September 2020)
Page(s) 256-262
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), 2024. Published by Science Publishing Group

Keywords

Burglar Crime, Generalized Poisson, Quasi Poisson, Dispersion, Count Data

References
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[3] Tammy, H. (2012). Modeling Underdispersed Count data with Generalized Poisson Regression. Biometrical Journal 12 (4): 8-11. doi: 10.1177/1536867X1201200412.
[4] İlknur Özmen. (2000). Quasi Likelihood/Moment Method for Generalized and Restricted Generalized Poisson Regression Models and Its Application. Biometrical Journal 42 (3), 303-314.
[5] Janguo. C. et al. (2019). Integrative Analysis of Spatial Heterogeneity and Overdispersion of Crime with Geographically Weighted Negative Binomial Model. International Journal of Geo-Information.
[6] Masengo, M. et al (2019). Borderland-related Crimes and Security threat in Kenya. National Crime Research Survey. Nairobi, Kenya.
[7] Antolos and Daniel. (2011). Investigating Factors Associated with Burglary Crime Analysis using Logistic Regression Modeling. Dissertation and Theses. 15.
[8] Consul, P. et. al (1988). Maximum likelihood estimation for the generalized Poisson distribution when sample mean is larger than sample variance. Communication Journal in Statistics Theory and Methods, 17 (1): 299-309.
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Author Information
  • Department of Statistics & Actuarial Science, Jomo Kenyatta University of Agriculture & Technology, Nairobi, Kenya

  • Department of Statistics & Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya

  • Department of Statistics & Actuarial Science, Jomo Kenyatta University of Agriculture & Technology, Nairobi, Kenya

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    Isaac Muchika, Antony Ngunyi, Thomas Mageto. (2020). Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya. American Journal of Theoretical and Applied Statistics, 9(5), 256-262. https://doi.org/10.11648/j.ajtas.20200905.19

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    ACS Style

    Isaac Muchika; Antony Ngunyi; Thomas Mageto. Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya. Am. J. Theor. Appl. Stat. 2020, 9(5), 256-262. doi: 10.11648/j.ajtas.20200905.19

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    AMA Style

    Isaac Muchika, Antony Ngunyi, Thomas Mageto. Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya. Am J Theor Appl Stat. 2020;9(5):256-262. doi: 10.11648/j.ajtas.20200905.19

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  • @article{10.11648/j.ajtas.20200905.19,
      author = {Isaac Muchika and Antony Ngunyi and Thomas Mageto},
      title = {Modeling Burglar Incidents Data Using Generalized and Quasi Poisson Regression Models: A Case Study of Nairobi City County, Kenya},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {9},
      number = {5},
      pages = {256-262},
      doi = {10.11648/j.ajtas.20200905.19},
      url = {https://doi.org/10.11648/j.ajtas.20200905.19},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20200905.19},
      abstract = {Serious violent crimes including Burglary, dangerous drug trafficking and sexual offenses make up the bulk of incidents filed at police stations daily. These crimes related activities poses a serious threat to the peace and serenity of a nation as far as safety is concerned. Burglar incidents data are often discrete and do not conform to the general assumptions of the linear model and its variants. Ordinarily, such data could be modeled using a linear regression approach to derive the relationship between the response variable to the underlying covariates. However, the narrowing of the gap between city and suburban burglar crime rates brings about variability invalidating the application of Ordinary linear regression approaches. The main objective of this study focused on the comparative use of Generalized Poisson and Quasi-Poisson models as an alternative to the classical linear regression approach in modeling Burglar incidents in Nairobi City County, Kenya. The prime advantage of applying Quasi Poisson in count data analysis is that it fixes the basic fallacy of assuming homogeneity in data and allows estimation of dispersion. The study used secondary data covering Eight (8) Nairobi's Administrative Divisions from the National Crime Research Center (NCRC) for the period 2016-2018. The comparison criteria were the Akaike Information (AIC) Criterion and Deviance Information Criterion (DIC) alongside other model diagnostics tests. Application of this results in burglar events revealed that the number of incidents in the study area are Under-dispersed with the risks of experiencing Burglar crime being above 5% in all the locations surveyed. In an attempt to explore Burglar to location relationship, results from study proved that Generalized Poisson Model performed better than the Quasi Poisson model having posted the lowest AIC value.},
     year = {2020}
    }
    

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  • TY  - JOUR
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    AU  - Antony Ngunyi
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    AB  - Serious violent crimes including Burglary, dangerous drug trafficking and sexual offenses make up the bulk of incidents filed at police stations daily. These crimes related activities poses a serious threat to the peace and serenity of a nation as far as safety is concerned. Burglar incidents data are often discrete and do not conform to the general assumptions of the linear model and its variants. Ordinarily, such data could be modeled using a linear regression approach to derive the relationship between the response variable to the underlying covariates. However, the narrowing of the gap between city and suburban burglar crime rates brings about variability invalidating the application of Ordinary linear regression approaches. The main objective of this study focused on the comparative use of Generalized Poisson and Quasi-Poisson models as an alternative to the classical linear regression approach in modeling Burglar incidents in Nairobi City County, Kenya. The prime advantage of applying Quasi Poisson in count data analysis is that it fixes the basic fallacy of assuming homogeneity in data and allows estimation of dispersion. The study used secondary data covering Eight (8) Nairobi's Administrative Divisions from the National Crime Research Center (NCRC) for the period 2016-2018. The comparison criteria were the Akaike Information (AIC) Criterion and Deviance Information Criterion (DIC) alongside other model diagnostics tests. Application of this results in burglar events revealed that the number of incidents in the study area are Under-dispersed with the risks of experiencing Burglar crime being above 5% in all the locations surveyed. In an attempt to explore Burglar to location relationship, results from study proved that Generalized Poisson Model performed better than the Quasi Poisson model having posted the lowest AIC value.
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