TY - GEN

T1 - Parameter Estimation and Hypothesis Testing of Multivariate Adaptive Bivariate Generalized Poisson Regression Spline

AU - Ramadany, Rizqiyanti

AU - Otok, Bambang Widjanarko

AU - Purhadi,

N1 - Publisher Copyright:
© 2023 American Institute of Physics Inc.. All rights reserved.

PY - 2023/1/27

Y1 - 2023/1/27

N2 - Poisson regression is a regression method used to model the count data. The response variable of Poisson regression has a Poisson distribution. Poisson regression assumes that the response variable average value is equal to the response variable variance value, called the equidispersion condition. Generalized Poisson Regression (GPR) is used to overcome that if the equidispersion assumption cannot be fulfilled. If there are two correlated responses variable, the modeling used Bivariate Generalized Poisson Regression (BGPR). Multivariate Adaptive Regression Spline (MARS) is a nonparametric regression method with flexibility in high-dimensional data. Multivariate Adaptive Bivariate Generalized Poisson Regression Spline (MABGPRS) is a development of the MARS method and BGPR method. This study will discuss parameter estimation and test statistics for the MABGPRS model. The estimation of the MABGPRS model parameters was carried out using Weighted Least Square (WLS) method and the Maximum Likelihood Estimation (MLE) method. MLE was not found analytical solution, so the estimation uses the Berndt-Hall-Hall-Hausman (BHHH) iteration method to solve it. The test statistics for simultaneous and using Maximum Likelihood Ratio Test (MLRT).

AB - Poisson regression is a regression method used to model the count data. The response variable of Poisson regression has a Poisson distribution. Poisson regression assumes that the response variable average value is equal to the response variable variance value, called the equidispersion condition. Generalized Poisson Regression (GPR) is used to overcome that if the equidispersion assumption cannot be fulfilled. If there are two correlated responses variable, the modeling used Bivariate Generalized Poisson Regression (BGPR). Multivariate Adaptive Regression Spline (MARS) is a nonparametric regression method with flexibility in high-dimensional data. Multivariate Adaptive Bivariate Generalized Poisson Regression Spline (MABGPRS) is a development of the MARS method and BGPR method. This study will discuss parameter estimation and test statistics for the MABGPRS model. The estimation of the MABGPRS model parameters was carried out using Weighted Least Square (WLS) method and the Maximum Likelihood Estimation (MLE) method. MLE was not found analytical solution, so the estimation uses the Berndt-Hall-Hall-Hausman (BHHH) iteration method to solve it. The test statistics for simultaneous and using Maximum Likelihood Ratio Test (MLRT).

UR - http://www.scopus.com/inward/record.url?scp=85147268589&partnerID=8YFLogxK

U2 - 10.1063/5.0106458

DO - 10.1063/5.0106458

M3 - Conference contribution

AN - SCOPUS:85147268589

T3 - AIP Conference Proceedings

BT - 3rd International Conference on Science, Mathematics, Environment, and Education

A2 - Indriyanti, Nurma Yunita

A2 - Sari, Meida Wulan

PB - American Institute of Physics Inc.

T2 - 3rd International Conference on Science, Mathematics, Environment, and Education: Flexibility in Research and Innovation on Science, Mathematics, Environment, and Education for Sustainable Development, ICoSMEE 2021

Y2 - 27 July 2021 through 28 July 2021

ER -