Published date: Mar 27 2024

Journal Title: KnE Life Sciences

Issue title: International Conference On Mathematics And Science Education (ICMScE 2022): Life Sciences

Pages: 186–196

DOI: 10.18502/kls.v8i1.15547

Christin NingrumDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, East Java, Indonesia

Purhadi .purhadi@statistika.its.ac.idDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, East Java, Indonesia

Sutikno .Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, East Java, Indonesia

When the response variable is discrete as a number (count) and there is a violation of the assumption of equidispersion, namely overdispersion or underdispersion then one of the appropriate alternative models used is Negative Binomial Regression (NBR). Moreover, if there are two correlated response variables and have an equidispersion violation, the Bivariate Negative Binomial Regression (BNBR) model is the solution. However, the BNBR model is considered inappropriate if the data contains spatial and temporal heterogeneity derived from panel data with the unit of observation in the form of a region. Therefore, a model is offered which is known as Geographically and Temporally Weighted Bivariate Negative Binomial Regression (GTWBNBR) which accommodates spatial and temporal effects. This study aims to conduct parameter estimates and test statistics for the GTWBNBR model. Estimated parameters use Maximum Likelihood Estimation (MLE) with BHHH numerical iteration because the MLE estimates are not closed-form. When the sample size is large, the Maximum Likelihood Ratio Test (MLRT) is used for simultaneous parameter testing while the test statistic for partial parameter testing approaches the Chi-Square distribution so that it can be tested using the Z-Test.

Keywords: parameter estimation, hypothesis testing, GTWBNBR

[1] Casella G, Berger RL. Statistical Inference. Inc. California: Wadsworth; 2021.

[2] Hilbe J. Negative binomial regression. Cambridge: Cambridge University Press; 2011. https://doi.org/10.1017/CBO9780511973420.

[3] Famoye F. On the bivariate negative binomial regression model. J Appl Stat. 2010;37(6):969–81.

[4] Omzen I, Famoye F. Count regression models with an application to zoological data containing structural zeros. J Appl Stat. 2007;5:491–502.

[5] Lawless JF. Negative binomial and mixed Poisson regression. Can J Stat. 1987;15(3):209–25.

[6] Cameron AC, Trivedi PK. Regression Analysis of Count Data. USA: Cambridge University Press; 2013. https://doi.org/10.1017/CBO9781139013567.

[7] R. Winkelmann and K.F. Zimmermann,.” Recent developments in count data modelling: theory and application.,” Journal of Economic Surveys. vol. 9, p.1995.

[8] Berk D, MacDonald J. Overdispersion and Poisson regression. J Quant Criminol. 2008;24(3):269–84.

[9] Brunsdon C, Fotheringham AS, Charlton ME. Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal. 1996;28(4):281–98.

[10] Zhao C, Jensen J, Weng Q, Weaver R. A geographically weighted regression analysis of the underlying factors related to the surface urban heat island phenomenon. Remote Sens (Basel). 2018;10(9):1428.

[11] Fitriani R, Jaya IG. “ Multilevel model of dengue disease transmission in West Java province, Indonesia by means INLA” Communications in Mathematical Biology and Neuroscience. p. 2020.

[12] F.N. Alfariz and Purhadi,.“Pemodelan jumlah anak putus sekolah usia wajib belajar dan jumlah wanita menikah dini di jawa timur dengan pendekatan geographically weighted bivariate negative binomial regression.,” Jurnal Sains Dan Seni ITS. vol. 8, pp. 193–199, 2020.

[13] Gomes MJ, Cunto F, da Silva AR. Geographically weighted negative binomial regression applied to zonal level safety performance models. Accid Anal Prev. 2017 Sep;106:254–61.

[14] Dewi YS, Purhadi S, Purnami SW. Comparison of Nelder Mead and BFGS Algorithms on Geographically Weighted Multivariate Negative Binomial. Int J Adv Sci Eng Inf Technol. 2019;9(3):979–87.

[15] Wasani D. “Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Gamma regression model.,” In: IOP Conference Series: Earth and Environmental Science. pp. 12044. IOP Publishing (2021).

[16] Huang B, Wu B, Barry M. Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices. Int J Geogr Inf Sci. 2010;24(3):383–401.

[17] Cheon SH, Jung BC. Tests for independence in a bivariate negative binomial model. J Korean Stat Soc. 2009;38(2):185–90.

[18] Fotheringham AS, Crespo R, Yao J. Geographical and temporal weighted regression (GTWR). Geogr Anal. 2015;47(4):431–52.

[19] Nakaya T, Fotheringham AS, Brunsdon C, Charlton M. Geographically weighted Poisson regression for disease association mapping. Stat Med. 2005 Sep;24(17):2695– 717.

[20] Lamusu TM, Machmud T, Resmawan R. Estimator Nadaraya-Watson dengan Pendekatan Cross Validation dan Generalized Cross Validation untuk Mengestimasi Produksi Jagung. Indonesian Journal of Applied Statistics. 2020;3(2):85–93.