Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data

Kipngetich Gideon; Anthony Wanjoya; Samuel Mwalili

doi:doi:10.11648/j.ijdsa.20190505.15

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Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data

Kipngetich Gideon, Anthony Wanjoya, Samuel Mwalili

Published in International Journal of Data Science and Analysis (Volume 5, Issue 5)

Received: 8 October 2019 Accepted: 23 October 2019 Published: 30 October 2019

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Abstract

To establish viable statistical model for modelling and analyzing DMFT index data which is important in oral health studies, difficulty arise when DMFT index data is characterized by over-dispersion. Over-dispersion caused by unobserved heterogeneity in the data pose a problem in fitting more common models to this data. and failure to account on such heterogeneity in the model can undermine the validity of the empirical results. The limitations of other count data models to account for overdispersion in DMFT index data due to existence of heterogeneity in the data, this paper formulated alternative model that captures heterogeneity in the data, that is Bayesian Finite mixture negative binomial regression model and the model applied to simulated overdispersed count data to determine the exact number of negative binomial components to be mixed and finally apply the model to DMFT index data. Bayesian finite mixture Negative Binomial (BFMNB-3) regression model is useful since the data were collected from heterogenous population. simulation results shows that 3-component Bayesian finite mixture of NB regression model converges and was quite enough to model the overdispersed simulated count data, applying BFMNB-3 model to DMFT index data, the model capability to capture heterogeneity in the data identifies that the methods; all the treatment (all methods together), mouth wash with 0.2% sodium fluoride and Oral hygiene were the best methods in preventing tooth decay in children in Belo Horizonte (Brazil) aged seven years this shows that BFMNB-3 performs better than BNB model were due to heterogeneity present in methods it only identifies methods; all the treatment (all methods together) and mouth wash with 0.2% sodium fluoride to be the best methods for preventing tooth decay for children in Belo Horizonte (Brazil) aged seven while this two methods were not the only significant methods, therefore from results there is complete superiority of BFMNB-3 over BNB model. R statistical software was used to accomplish the objectives of this paper.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 5)
DOI	10.11648/j.ijdsa.20190505.15
Page(s)	104-110
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), 2019. Published by Science Publishing Group

Keywords

BFMNB-3 Model, DMFT Index Data, BNB

References

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APA Style

Kipngetich Gideon, Anthony Wanjoya, Samuel Mwalili. (2019). Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. International Journal of Data Science and Analysis, 5(5), 104-110. https://doi.org/10.11648/j.ijdsa.20190505.15

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ACS Style

Kipngetich Gideon; Anthony Wanjoya; Samuel Mwalili. Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. Int. J. Data Sci. Anal. 2019, 5(5), 104-110. doi: 10.11648/j.ijdsa.20190505.15

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AMA Style

Kipngetich Gideon, Anthony Wanjoya, Samuel Mwalili. Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. Int J Data Sci Anal. 2019;5(5):104-110. doi: 10.11648/j.ijdsa.20190505.15

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@article{10.11648/j.ijdsa.20190505.15,
  author = {Kipngetich Gideon and Anthony Wanjoya and Samuel Mwalili},
  title = {Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {104-110},
  doi = {10.11648/j.ijdsa.20190505.15},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.15},
  abstract = {To establish viable statistical model for modelling and analyzing DMFT index data which is important in oral health studies, difficulty arise when DMFT index data is characterized by over-dispersion. Over-dispersion caused by unobserved heterogeneity in the data pose a problem in fitting more common models to this data. and failure to account on such heterogeneity in the model can undermine the validity of the empirical results. The limitations of other count data models to account for overdispersion in DMFT index data due to existence of heterogeneity in the data, this paper formulated alternative model that captures heterogeneity in the data, that is Bayesian Finite mixture negative binomial regression model and the model applied to simulated overdispersed count data to determine the exact number of negative binomial components to be mixed and finally apply the model to DMFT index data. Bayesian finite mixture Negative Binomial (BFMNB-3) regression model is useful since the data were collected from heterogenous population. simulation results shows that 3-component Bayesian finite mixture of NB regression model converges and was quite enough to model the overdispersed simulated count data, applying BFMNB-3 model to DMFT index data, the model capability to capture heterogeneity in the data identifies that the methods; all the treatment (all methods together), mouth wash with 0.2% sodium fluoride and Oral hygiene were the best methods in preventing tooth decay in children in Belo Horizonte (Brazil) aged seven years this shows that BFMNB-3 performs better than BNB model were due to heterogeneity present in methods it only identifies methods; all the treatment (all methods together) and mouth wash with 0.2% sodium fluoride to be the best methods for preventing tooth decay for children in Belo Horizonte (Brazil) aged seven while this two methods were not the only significant methods, therefore from results there is complete superiority of BFMNB-3 over BNB model. R statistical software was used to accomplish the objectives of this paper.},
 year = {2019}
}

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TY  - JOUR
T1  - Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data
AU  - Kipngetich Gideon
AU  - Anthony Wanjoya
AU  - Samuel Mwalili
Y1  - 2019/10/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190505.15
DO  - 10.11648/j.ijdsa.20190505.15
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 104
EP  - 110
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190505.15
AB  - To establish viable statistical model for modelling and analyzing DMFT index data which is important in oral health studies, difficulty arise when DMFT index data is characterized by over-dispersion. Over-dispersion caused by unobserved heterogeneity in the data pose a problem in fitting more common models to this data. and failure to account on such heterogeneity in the model can undermine the validity of the empirical results. The limitations of other count data models to account for overdispersion in DMFT index data due to existence of heterogeneity in the data, this paper formulated alternative model that captures heterogeneity in the data, that is Bayesian Finite mixture negative binomial regression model and the model applied to simulated overdispersed count data to determine the exact number of negative binomial components to be mixed and finally apply the model to DMFT index data. Bayesian finite mixture Negative Binomial (BFMNB-3) regression model is useful since the data were collected from heterogenous population. simulation results shows that 3-component Bayesian finite mixture of NB regression model converges and was quite enough to model the overdispersed simulated count data, applying BFMNB-3 model to DMFT index data, the model capability to capture heterogeneity in the data identifies that the methods; all the treatment (all methods together), mouth wash with 0.2% sodium fluoride and Oral hygiene were the best methods in preventing tooth decay in children in Belo Horizonte (Brazil) aged seven years this shows that BFMNB-3 performs better than BNB model were due to heterogeneity present in methods it only identifies methods; all the treatment (all methods together) and mouth wash with 0.2% sodium fluoride to be the best methods for preventing tooth decay for children in Belo Horizonte (Brazil) aged seven while this two methods were not the only significant methods, therefore from results there is complete superiority of BFMNB-3 over BNB model. R statistical software was used to accomplish the objectives of this paper.
VL  - 5
IS  - 5
ER  -

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Author Information

Kipngetich Gideon

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Samuel Mwalili

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

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Plain Text BibTeX RIS

APA Style

Kipngetich Gideon, Anthony Wanjoya, Samuel Mwalili. (2019). Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. International Journal of Data Science and Analysis, 5(5), 104-110. https://doi.org/10.11648/j.ijdsa.20190505.15

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ACS Style

Kipngetich Gideon; Anthony Wanjoya; Samuel Mwalili. Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. Int. J. Data Sci. Anal. 2019, 5(5), 104-110. doi: 10.11648/j.ijdsa.20190505.15

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AMA Style

Kipngetich Gideon, Anthony Wanjoya, Samuel Mwalili. Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data. Int J Data Sci Anal. 2019;5(5):104-110. doi: 10.11648/j.ijdsa.20190505.15

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@article{10.11648/j.ijdsa.20190505.15,
  author = {Kipngetich Gideon and Anthony Wanjoya and Samuel Mwalili},
  title = {Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {104-110},
  doi = {10.11648/j.ijdsa.20190505.15},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.15},
  abstract = {To establish viable statistical model for modelling and analyzing DMFT index data which is important in oral health studies, difficulty arise when DMFT index data is characterized by over-dispersion. Over-dispersion caused by unobserved heterogeneity in the data pose a problem in fitting more common models to this data. and failure to account on such heterogeneity in the model can undermine the validity of the empirical results. The limitations of other count data models to account for overdispersion in DMFT index data due to existence of heterogeneity in the data, this paper formulated alternative model that captures heterogeneity in the data, that is Bayesian Finite mixture negative binomial regression model and the model applied to simulated overdispersed count data to determine the exact number of negative binomial components to be mixed and finally apply the model to DMFT index data. Bayesian finite mixture Negative Binomial (BFMNB-3) regression model is useful since the data were collected from heterogenous population. simulation results shows that 3-component Bayesian finite mixture of NB regression model converges and was quite enough to model the overdispersed simulated count data, applying BFMNB-3 model to DMFT index data, the model capability to capture heterogeneity in the data identifies that the methods; all the treatment (all methods together), mouth wash with 0.2% sodium fluoride and Oral hygiene were the best methods in preventing tooth decay in children in Belo Horizonte (Brazil) aged seven years this shows that BFMNB-3 performs better than BNB model were due to heterogeneity present in methods it only identifies methods; all the treatment (all methods together) and mouth wash with 0.2% sodium fluoride to be the best methods for preventing tooth decay for children in Belo Horizonte (Brazil) aged seven while this two methods were not the only significant methods, therefore from results there is complete superiority of BFMNB-3 over BNB model. R statistical software was used to accomplish the objectives of this paper.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Finite Mixture Negative Binomial Model for Over-dispersed Count Data with Application to DMFT Index Data
AU  - Kipngetich Gideon
AU  - Anthony Wanjoya
AU  - Samuel Mwalili
Y1  - 2019/10/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190505.15
DO  - 10.11648/j.ijdsa.20190505.15
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 104
EP  - 110
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190505.15
AB  - To establish viable statistical model for modelling and analyzing DMFT index data which is important in oral health studies, difficulty arise when DMFT index data is characterized by over-dispersion. Over-dispersion caused by unobserved heterogeneity in the data pose a problem in fitting more common models to this data. and failure to account on such heterogeneity in the model can undermine the validity of the empirical results. The limitations of other count data models to account for overdispersion in DMFT index data due to existence of heterogeneity in the data, this paper formulated alternative model that captures heterogeneity in the data, that is Bayesian Finite mixture negative binomial regression model and the model applied to simulated overdispersed count data to determine the exact number of negative binomial components to be mixed and finally apply the model to DMFT index data. Bayesian finite mixture Negative Binomial (BFMNB-3) regression model is useful since the data were collected from heterogenous population. simulation results shows that 3-component Bayesian finite mixture of NB regression model converges and was quite enough to model the overdispersed simulated count data, applying BFMNB-3 model to DMFT index data, the model capability to capture heterogeneity in the data identifies that the methods; all the treatment (all methods together), mouth wash with 0.2% sodium fluoride and Oral hygiene were the best methods in preventing tooth decay in children in Belo Horizonte (Brazil) aged seven years this shows that BFMNB-3 performs better than BNB model were due to heterogeneity present in methods it only identifies methods; all the treatment (all methods together) and mouth wash with 0.2% sodium fluoride to be the best methods for preventing tooth decay for children in Belo Horizonte (Brazil) aged seven while this two methods were not the only significant methods, therefore from results there is complete superiority of BFMNB-3 over BNB model. R statistical software was used to accomplish the objectives of this paper.
VL  - 5
IS  - 5
ER  -

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