Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model

Enas Gawdat Yehia

doi:doi:10.11648/j.ajtas.20211003.13

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Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model

Enas Gawdat Yehia

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 3)

Received: 18 May 2021 Accepted: 11 June 2021 Published: 21 June 2021

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Abstract

Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.

Published in	American Journal of Theoretical and Applied Statistics (Volume 10, Issue 3)
DOI	10.11648/j.ajtas.20211003.13
Page(s)	152-157
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), 2021. Published by Science Publishing Group

Keywords

Count Regression, Zero-Truncated Poisson, Overdispersion, Likelihood Ratio Test, Score Test, Wald Test

References

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APA Style

Enas Gawdat Yehia. (2021). Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. American Journal of Theoretical and Applied Statistics, 10(3), 152-157. https://doi.org/10.11648/j.ajtas.20211003.13

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ACS Style

Enas Gawdat Yehia. Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. Am. J. Theor. Appl. Stat. 2021, 10(3), 152-157. doi: 10.11648/j.ajtas.20211003.13

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AMA Style

Enas Gawdat Yehia. Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. Am J Theor Appl Stat. 2021;10(3):152-157. doi: 10.11648/j.ajtas.20211003.13

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@article{10.11648/j.ajtas.20211003.13,
  author = {Enas Gawdat Yehia},
  title = {Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {3},
  pages = {152-157},
  doi = {10.11648/j.ajtas.20211003.13},
  url = {https://doi.org/10.11648/j.ajtas.20211003.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211003.13},
  abstract = {Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.},
 year = {2021}
}

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TY  - JOUR
T1  - Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model
AU  - Enas Gawdat Yehia
Y1  - 2021/06/21
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211003.13
DO  - 10.11648/j.ajtas.20211003.13
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  - 152
EP  - 157
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211003.13
AB  - Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.
VL  - 10
IS  - 3
ER  -

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Author Information

Enas Gawdat Yehia

Department of Statistics, Faculty of Commerce, Al-Azhar University, Tafahna Al-Ashraf, Egypt

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Enas Gawdat Yehia. (2021). Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. American Journal of Theoretical and Applied Statistics, 10(3), 152-157. https://doi.org/10.11648/j.ajtas.20211003.13

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ACS Style

Enas Gawdat Yehia. Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. Am. J. Theor. Appl. Stat. 2021, 10(3), 152-157. doi: 10.11648/j.ajtas.20211003.13

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AMA Style

Enas Gawdat Yehia. Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model. Am J Theor Appl Stat. 2021;10(3):152-157. doi: 10.11648/j.ajtas.20211003.13

Copy | Download

@article{10.11648/j.ajtas.20211003.13,
  author = {Enas Gawdat Yehia},
  title = {Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {3},
  pages = {152-157},
  doi = {10.11648/j.ajtas.20211003.13},
  url = {https://doi.org/10.11648/j.ajtas.20211003.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211003.13},
  abstract = {Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model
AU  - Enas Gawdat Yehia
Y1  - 2021/06/21
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211003.13
DO  - 10.11648/j.ajtas.20211003.13
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  - 152
EP  - 157
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211003.13
AB  - Poisson regression is the most extensively used model for modeling data that are measured as counts. The main characteristic of Poisson regression model is the equidispersion limitation in which the mean and variance of the count variable are the same. However, in many situations the variance of the count variable is greater than the mean which causes overdispersion, and hence, poor fit will be resulted when inference about regression parameters. Alternatively, the negative binomial regression is preferred when overdispersion is present. In addition, in particular cases, the zero counts are not observed in data which is known as zero-truncation. In the presence of overdispersion in zero-truncated count data, the zero-truncated negative binomial (ZTNB) regression model can be used as an alternative to zero-truncated Poisson (ZTP) regression model. In this paper, for testing overdispersion in ZTNB regression model against ZTP regression model, the likelihood ratio test (LRT), score test, and Wald test are proposed. A Monte-Carlo simulation is carried out in order to examine the empirical power for statistics of these tests under different levels of overdispersion and various sample sizes. The simulation results indicate that Wald test is more powerful than the LRT and score test for detecting the overdispersion parameter in ZTNB regression model against ZTP regression model, since it provides the highest statistical power. Thus, the Wald test is preferable for detecting the overdispersion problem in zero-truncated count data.
VL  - 10
IS  - 3
ER  -

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