TY - GEN

T1 - Parameter estimation and statistical test of geographically weighted bivariate Poisson inverse Gaussian regression models

AU - Amalia, Junita

AU - Purhadi,

AU - Otok, Bambang Widjanarko

N1 - Publisher Copyright:
© 2017 Author(s).

PY - 2017/11/22

Y1 - 2017/11/22

N2 - Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (over-dispersion). The ignorance of over-dispersion causes underestimates in standard error. Furthermore, it causes incorrect decision in the statistical test. Previously, paired count data has a correlation and it has bivariate Poisson distribution. If there is over-dispersion, modeling paired count data is not sufficient with simple bivariate Poisson regression. Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mix Poisson regression for modeling paired count data within over-dispersion. BPIGR model produces a global model for all locations. In another hand, each location has different geographic conditions, social, cultural and economic so that Geographically Weighted Regression (GWR) is needed. The weighting function of each location in GWR generates a different local model. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve over-dispersion and to generate local models. Parameter estimation of GWBPIGR model obtained by Maximum Likelihood Estimation (MLE) method. Meanwhile, hypothesis testing of GWBPIGR model acquired by Maximum Likelihood Ratio Test (MLRT) method.

AB - Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (over-dispersion). The ignorance of over-dispersion causes underestimates in standard error. Furthermore, it causes incorrect decision in the statistical test. Previously, paired count data has a correlation and it has bivariate Poisson distribution. If there is over-dispersion, modeling paired count data is not sufficient with simple bivariate Poisson regression. Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mix Poisson regression for modeling paired count data within over-dispersion. BPIGR model produces a global model for all locations. In another hand, each location has different geographic conditions, social, cultural and economic so that Geographically Weighted Regression (GWR) is needed. The weighting function of each location in GWR generates a different local model. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve over-dispersion and to generate local models. Parameter estimation of GWBPIGR model obtained by Maximum Likelihood Estimation (MLE) method. Meanwhile, hypothesis testing of GWBPIGR model acquired by Maximum Likelihood Ratio Test (MLRT) method.

UR - http://www.scopus.com/inward/record.url?scp=85036613963&partnerID=8YFLogxK

U2 - 10.1063/1.5012224

DO - 10.1063/1.5012224

M3 - Conference contribution

AN - SCOPUS:85036613963

T3 - AIP Conference Proceedings

BT - Proceedings of the 13th IMT-GT International Conference on Mathematics, Statistics and their Applications, ICMSA 2017

A2 - Ibrahim, Haslinda

A2 - Aziz, Nazrina

A2 - Nawawi, Mohd Kamal Mohd

A2 - Rohni, Azizah Mohd

A2 - Zulkepli, Jafri

PB - American Institute of Physics Inc.

T2 - 13th IMT-GT International Conference on Mathematics, Statistics and their Applications, ICMSA 2017

Y2 - 4 December 2017 through 7 December 2017

ER -