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

Junita Amalia*, Purhadi, Bambang Widjanarko Otok

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 13th IMT-GT International Conference on Mathematics, Statistics and their Applications, ICMSA 2017
EditorsHaslinda Ibrahim, Nazrina Aziz, Mohd Kamal Mohd Nawawi, Azizah Mohd Rohni, Jafri Zulkepli
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735415959
DOIs
Publication statusPublished - 22 Nov 2017
Event13th IMT-GT International Conference on Mathematics, Statistics and their Applications, ICMSA 2017 - Kedah, Malaysia
Duration: 4 Dec 20177 Dec 2017

Publication series

NameAIP Conference Proceedings
Volume1905
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference13th IMT-GT International Conference on Mathematics, Statistics and their Applications, ICMSA 2017
Country/TerritoryMalaysia
CityKedah
Period4/12/177/12/17

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