Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse

John Kung’u; Leo Odongo; Ananda Kube

doi:doi:10.11648/j.ajtas.20221102.11

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Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse

John Kung’u, Leo Odongo, Ananda Kube

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 2)

Received: 20 January 2022 Accepted: 4 March 2022 Published: 12 March 2022

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Abstract

The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 2)
DOI	10.11648/j.ajtas.20221102.11
Page(s)	58-74
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

Correlated Zero Inflated Dynamic Panel Ordered Probit Model (ZIDPOPC), State Dependence, Unobserved Heterogeneity and Initial Condition Problem

References

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APA Style

John Kung’u, Leo Odongo, Ananda Kube. (2022). Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. American Journal of Theoretical and Applied Statistics, 11(2), 58-74. https://doi.org/10.11648/j.ajtas.20221102.11

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ACS Style

John Kung’u; Leo Odongo; Ananda Kube. Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. Am. J. Theor. Appl. Stat. 2022, 11(2), 58-74. doi: 10.11648/j.ajtas.20221102.11

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AMA Style

John Kung’u, Leo Odongo, Ananda Kube. Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. Am J Theor Appl Stat. 2022;11(2):58-74. doi: 10.11648/j.ajtas.20221102.11

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@article{10.11648/j.ajtas.20221102.11,
  author = {John Kung’u and Leo Odongo and Ananda Kube},
  title = {Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {2},
  pages = {58-74},
  doi = {10.11648/j.ajtas.20221102.11},
  url = {https://doi.org/10.11648/j.ajtas.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221102.11},
  abstract = {The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.},
 year = {2022}
}

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TY  - JOUR
T1  - Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse
AU  - John Kung’u
AU  - Leo Odongo
AU  - Ananda Kube
Y1  - 2022/03/12
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221102.11
DO  - 10.11648/j.ajtas.20221102.11
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  - 58
EP  - 74
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221102.11
AB  - The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.
VL  - 11
IS  - 2
ER  -

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Author Information

John Kung’u

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Leo Odongo

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya
Ananda Kube

Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya

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APA Style

John Kung’u, Leo Odongo, Ananda Kube. (2022). Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. American Journal of Theoretical and Applied Statistics, 11(2), 58-74. https://doi.org/10.11648/j.ajtas.20221102.11

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ACS Style

John Kung’u; Leo Odongo; Ananda Kube. Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. Am. J. Theor. Appl. Stat. 2022, 11(2), 58-74. doi: 10.11648/j.ajtas.20221102.11

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AMA Style

John Kung’u, Leo Odongo, Ananda Kube. Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse. Am J Theor Appl Stat. 2022;11(2):58-74. doi: 10.11648/j.ajtas.20221102.11

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@article{10.11648/j.ajtas.20221102.11,
  author = {John Kung’u and Leo Odongo and Ananda Kube},
  title = {Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {2},
  pages = {58-74},
  doi = {10.11648/j.ajtas.20221102.11},
  url = {https://doi.org/10.11648/j.ajtas.20221102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221102.11},
  abstract = {The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Classical Approach to Zero-Inflated Dynamic Panel Ordered Probit Model with an Application in Drug Abuse
AU  - John Kung’u
AU  - Leo Odongo
AU  - Ananda Kube
Y1  - 2022/03/12
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221102.11
DO  - 10.11648/j.ajtas.20221102.11
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  - 58
EP  - 74
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221102.11
AB  - The Zero inflated ordered categorical data with time series structure are often a characteristic of behavioral research attributed to non-participation decision and zero consumption of substance such as drugs among the participants. The existing Semi-parametric zero inflated dynamic panel probit model with selectivity have exhibited biasness and inconsistency in estimators as a result of poor treatment of initial condition and exclusion of selectivity in the unobserved individual effects respectively. The model assumed that the cut points are known to address heaping in the data and therefore cannot be used when the cut points are unknown. In this paper, a Zero inflated dynamic panel ordered probit models have been developed to address the above challenges. Average partial effects that presents the impacts on the specific probabilities per unit change in the covariates are also given. Since the solutions are not of closed form, Maximum likelihood estimation based on Newton Raphson algorithm was used to estimate the parameters of the model. A Monte Carlo study was carried out to investigate some theoretical properties of the estimators in the models. The study found that the Zero inflated dynamic panel ordered probit models with independent and correlated error terms produced consistent estimators. The Zero inflated dynamic panel ordered probit models with independent and correlated error terms had more accurate estimators than the Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with correlated error terms fitted the National Longitudinal Survey of Youth 1997 better than Zero inflated dynamic panel ordered probit model with independent error terms and Dynamic panel ordered probit model. The Zero inflated dynamic panel ordered probit model with independent error terms fitted the National Longitudinal Survey of Youth 1997 better the Dynamic panel ordered probit model.
VL  - 11
IS  - 2
ER  -

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