Count time series with excess zeros: A Bayesian perspective using zero-adjusted distributions

Luiz Otávio de Oliveira Pala; Marcela de Marillac Carvalho; Thelma Sáfadi

doi:10.5433/1679-0375.2022v43n2p147

Séries temporais de contagem com excesso de zeros: Uma perspectiva Bayesiana utilizando distribuições zero-ajustadas

Autores

Luiz Otávio de Oliveira Pala Universidade Federal de Lavras - - UFLA https://orcid.org/0000-0002-9941-7951
Marcela de Marillac Carvalho Universidade Federal de Lavras - UFAL https://orcid.org/0000-0001-5998-5551
Thelma Sáfadi Universidade Federal de Lavras - UFLA https://orcid.org/0000-0002-4918-300X

DOI:

https://doi.org/10.5433/1679-0375.2022v43n2p147

Palavras-chave:

ARMA(p, q) process , Count data , Metropolis-hastings

Resumo

Modelos para dados de contagem temporalmente correlacionados tem sido estudados utilizando diversas distribuicoes condicionais, como a Poisson, e com a insercao de diferentes estruturas de dependencia. No entanto, os fenomenos de contagem podem apresentar caracteristicas como excesso de zeros e alta dispersao, que devem ser levadas em consideracao durante a modelagem e escolha de uma distribuicao condicional. Estetrabalho tem como objetivo estudar modelos para series de contagem utilizando tres distribuicoes condicionais zero-ajustadas com estruturas de dependencia na forma ARMA(p, q), em uma perspectiva via inferencia Bayesiana. De forma geral, foi realizado um breve estudo de simulacao a partir da analise Bayesiana proposta e a serie temporal do numero de obitos em decorrencia de febre hemorragica causada pelo virus da dengue (CID-A91) no Brasil foi analisada.

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Biografia do Autor

Luiz Otávio de Oliveira Pala, Universidade Federal de Lavras - - UFLA

Doutorando em Estatística e Experimentação Agrícola, UFLA, Lavras, MG

Marcela de Marillac Carvalho, Universidade Federal de Lavras - UFAL

Doutoranda em Estatística e Experimentação Agrícola, UFLA, Lavras, MG

Thelma Sáfadi, Universidade Federal de Lavras - UFLA

Prof. Dr., Departamento de Estatística, UFLA, Lavras, MG

Referências

ANDRADE, B.; ANDRADE, M.; EHLERS, R. Bayesian GARMA models for count data. Communications in statistics: case studies, data analysis and applications, Philadelphia, v. 1, n. 4, p. 192-205, 2015. DOI: https://doi.org/10.1080/23737484.2016.1190307. DOI: https://doi.org/10.1080/23737484.2016.1190307

ALQAWBA, M.; DIAWARA, N.; CHAGANTY, N. Zero-inflated count time series models using Gaussian copula. Sequential Analysis, New York, v. 38, n. 3, p. 342-357, 2019. DOI: https://doi.org/10.1080/07474946.2019.1648922. DOI: https://doi.org/10.1080/07474946.2019.1648922

BARRETO-SOUZA, W. Mixed Poisson INAR(1) processes. Statistical papers, [London], v. 60, n. 6, p. 2119-2139, 2017. DOI: https://doi.org/ 10.1007/s00362-017-0912-x. DOI: https://doi.org/10.1007/s00362-017-0912-x

BENJAMIN, M.; RIGBY, R.; STASINOPOULOS, M. Generalized autoregressive moving average models. Journal of the American Statistical Association, Washington, v. 98, n. 461, p. 214-223, 2003. DOI: https://doi.org/10.1198/016214503388619238. DOI: https://doi.org/10.1198/016214503388619238

BOX, G.; PIERCE, D. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, Washington, v. 65, n. 332, p. 1509-1526, 1970. DOI: https://doi.org/10.2307/2284333. DOI: https://doi.org/10.1080/01621459.1970.10481180

BRASIL. Ministério da Saúde. Mortalidade - Brasil. Brasília: MS, [2022]. Available from: http://tabnet.datasus.gov.br/. Access in: Jan. 2022.

BROEK, J. A score test for zero inflation in a Poisson distribution. Biometrics, New York, n. 1, p. 738-743, 1995. DOI: https://doi.org/10.2307/2532959. DOI: https://doi.org/10.2307/2532959

BROEMELING, L. Bayesian analysis of time series. New York: CRC Press, 2019. DOI: https://doi.org/10.1201/9780429488443

CANOVA, F.; HANSEN, B. Are seasonal patterns constant over time? a test for seasonal stability. Journal of Business & Economic Statistics, Washington, v. 13, n. 3, p. 237-252, 1995. DOI: https://doi.org/10.2307/1392184. DOI: https://doi.org/10.1080/07350015.1995.10524598

CHIVERS, C. MHadaptive: General Markov chain Monte Carlo for Bayesian inference using adaptive Metropolis-Hastings sampling. 2015. Available from: https://CRAN.R-project.org/package=MHadaptive. Access in: Jan. 2022.

COX, D.; STUART, A. Some quick sign tests for trend in location and dispersion. Biometrika, Oxford, v. 42, n. 1/2, p. 80-95, 1955. DOI: https://doi.org/10.2307/2333424. DOI: https://doi.org/10.1093/biomet/42.1-2.80

DUANE, S.; KENNEDY, A.; PENDLETON, B.; ROWETH, D. Hybrid Monte Carlo. Physics letters B, Amsterdam, v. 195, n. 2, p. 216-222, 1987. DOI: https://doi.org/10.1016/0370-2693(87)91197-X. DOI: https://doi.org/10.1016/0370-2693(87)91197-X

FENG, C. A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. Journal of Statistical Distributions and Applications, Heidelberg, v. 8, n. 1, p. 1-19, 2021. DOI: https://doi.org/10.1186/s40488-021-00121-4. DOI: https://doi.org/10.1186/s40488-021-00121-4

GEWEKE, J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Staff Report, [s. l.], n. 148, p. 1-29, 1991. DOI: https://doi.org/10.21034/sr.148

GHAHRAMANI, M.; WHITE, S. Time series regression for zero-inflated and over dispersed count data: a functional response model approach. Journal of statistical theory and practice, Greensboro, v. 14, n. 2, p. 1-18, 2020. DOI: https://doi.org/10.1007/s42519-020-00094-8. DOI: https://doi.org/10.1007/s42519-020-00094-8

GONÇALVES, J.; BARRETO-SOUZA, W. Flexible regression models for counts with high-inflation of zeros. Metron, [s. l.], v. 78, n. 1, p. 71-95, 2020. DOI: https://doi.org/10.1007/s40300-020-00163-9. DOI: https://doi.org/10.1007/s40300-020-00163-9

HASHIM, L.; HASHIM, K.; SHIKER, M. An application comparison of two Poisson models on zero count data. Journal of Physics, [Bristol], v. 1818, n. 1, 2021. DOI: https://doi.org/10.1088/1742- 6596/1818/1/012165. DOI: https://doi.org/10.1088/1742-6596/1818/1/012165

HEIDELBERGER, P.; WELCH, P. Simulation run length control in the presence of an initial transient. Operations Research, Switzerland, v. 31, n. 6, p. 1109-1144, 1983. DOI: https://doi.org/0030- 364X/83/3106-1109 $01.25. DOI: https://doi.org/10.1287/opre.31.6.1109

HILBE, J. Modeling count data. Cambridge: Cambridge University Press, 2014. DOI: https://doi.org/10.1017/CBO9781139236065

KORENEV, B. Bessel functions and their applications. New York: CRC Press, 2002. DOI: https://doi.org/10.1201/b12551

LAMBERT, D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, Richmond v. 34, n. 1, p. 1-14, 1992. DOI: https://doi.org/10.2307/1269547. DOI: https://doi.org/10.2307/1269547

LÜDECKE, D.; BEN-SHACHAR, M.; PATIL, I.; WAGGONER, P.; MAKOWSKI, D. An R package for assessment, comparison and testing of statistical models. Journal of Open Source Software, Chicago, v. 6, n. 60, p. 31-39, 2021. DOI 10.21105/joss.03139. DOI: https://doi.org/10.21105/joss.03139

MULLAHY, J. Specification and testing of some modified count data models. Journal of Econometrics, Amsterdam, v. 33. n. 3, p. 341-365, 1986. DOI: https://doi.org/10.1016/0304-4076(86)90002-3. DOI: https://doi.org/10.1016/0304-4076(86)90002-3

NELDER, J.; WEDDERBURN, R. Generalized linear models. Journal of the Royal Statistical Society, London, v. 135, p. 370-384, 1972. DOI: https://doi.org/10.2307/2344614. DOI: https://doi.org/10.2307/2344614

PAYNE, E.; HARDIN, J.; EGEDE, L.; RAMAKRISH- NAN, V.;SELASSIE, A.; GEBREGZIABHER, M. Approaches for dealing with various sources of over dispersion in modeling count data: Scale adjustment versus modeling. Statistical Methods in Medical Research, Singapore v. 26, n. 4, p. 1802-1823, 2017. DOI: https://doi.org/10.1177/0962280215588569. DOI: https://doi.org/10.1177/0962280215588569

RAFTERY, A.; LEWIS, S. Comment: One long run with diagnostics: implementation strategies for Markov chain Monte Carlo. Statistical Science, [Commack], v. 7, n. 4, p. 493-497, 1992. DOI: https://doi.org/10.1214/ss/1177011143. DOI: https://doi.org/10.1214/ss/1177011143

RIGBY, R.; STASINOPOULOS, M.; HELLER, G.; DE BASTIANI, F. Distributions for modeling location, scale, and shape. New York: Chapman and Hall: CRC, 2019. DOI: https://doi.org/10.1201/9780429298547

ROBERT, C. Modified Bessel functions and their applications in probability and statistics. Statistics & Probability Letters, Amsterdam, v. 9, n. 2, p. 155-161, 1990. DOI: https://doi.org/10.1016/0167- 7152(92)90011-S. DOI: https://doi.org/10.1016/0167-7152(92)90011-S

ROCHA, A.; CRIBARI-NETO, F. Beta autoregressive moving average models. Test, [London], v. 18, n. 3, p. 529-545, 2009. DOI: https://doi.org/10.1007/s11749-008-0112-z. DOI: https://doi.org/10.1007/s11749-008-0112-z

SÁFADI, T.; MORETTIN, P. A Bayesian analysis of autoregressive models with random normal coefficients. Journal of Statistical Computation and Simulation, Philadelphia, v. 73, n. 8, p. 563-573, 2003. DOI: https://doi.org/10.1080/0094965031000136003. DOI: https://doi.org/10.1080/0094965031000136003

SATHISH, V.; MUKHOPADHYAY, S.; TIWARI, R. Autoregressive and moving average models for zero-inflated count time series. Statistica Neerlandica, Gravenhage, v. 76, n. 2, p. 190-218, 2021. DOI: https://doi.org/10.1111/stan.12255. DOI: https://doi.org/10.1111/stan.12255

STASINOPOULOS, M.; RIGBY, R. Gamlss dist: distributions for generalized additive models for location scale and shape. 2020. Available from: https://cran.r-project.org/web/packages/gamlss.dist/gamlss.dist.pdf. Access in: Jan. 2022.

TAWIAH, K.; IDDRISU, W.; ASOSEGA, K. Zero inflated time series modelling of COVID-19 deaths in Ghana. Journal of Environmental and Public health, New York, v. 2021, p. 1-9, 2021. DOI 10.1155/2021/5543977. DOI: https://doi.org/10.1155/2021/5543977

WORLD HEALTH ORGANIZATION. ICD-10: International statistical classification of dis- eases and related health problems. 2. nd. Geneva: WHO, 2004. Available from: https://apps.who.int/iris/handle/10665/42980. Access in: Nov. 2022.

YANG, M.; ZAMBA, G.; CAVANAUGH, J. Markov regression models for count time series with excess zeros: a partial likelihood approach. Statistical Methodology, [London], v. 14, p. 26-38, 2013. DOI: https://doi.org/10.1016/j.stamet.2013.02.001. DOI: https://doi.org/10.1016/j.stamet.2013.02.001

ZUO, G.; FU, K.; DAI, X.; ZHANG, L. Generalized poisson hurdle model for count data and its application in ear disease. Entropy, Basel, v. 23, n. 9, p. 1-16, 2021. DOI: https://doi.org/10.3390/e23091206. DOI: https://doi.org/10.3390/e23091206

ZUUR, A.; IENO, E.; WALKER, N.; SAVELIEV, A.; SMITH, G. Mixed effects models and extensions in ecology with R. New York: Springer, 2009. DOI: https://doi.org/10.1007/978-0-387-87458-6