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

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), 2022. 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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[6] Jinzhong, W., Wenji, F., and Wencheng. W. (2020) A Zero-Inflated Ordered Probit Model to Analyze Hazmat Truck Drivers' Violation Behavior and Associated Risk Factors. Open Access Journal, Vol 8, 110974-110985.
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[16] Christelis, D., and Galdeano, S. A. (2009). Smoking persistence across countries: An analysis using semi-parametric dynamic panel data models with selectivity. Journal of Applied Econometrics, 15, 334-360.
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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
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    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
  • Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya

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

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

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