scholarly journals Parameter Estimation and Hypothesis Testing of Geographically Weighted Multivariate Generalized Poisson Regression

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1523
Author(s):  
Sarni Maniar Berliana ◽  
Purhadi ◽  
Sutikno ◽  
Santi Puteri Rahayu
Keyword(s):  
Maximum Likelihood ◽  
Poisson Regression ◽  
Multivariate Regression ◽  
Ratio Test ◽  
Multivariate Regression Model ◽  
Generalized Poisson ◽  
Regression Parameters ◽  
Step Procedure ◽  
Generalized Poisson Regression ◽  
Maximum Likelihood Ratio Test

We introduce a new multivariate regression model based on the generalized Poisson distribution, which we called geographically-weighted multivariate generalized Poisson regression (GWMGPR) model, and we present a maximum likelihood step-by-step procedure to obtain parameters for it. We use the maximum likelihood ratio test to examine the significance of the regression parameters and to define their critical region.

scholarly journals Model Generalized Poisson Regression (GPR) dan Penerapannya pada Angka Pengangguran bagi Penduduk Usia Kerja di Provinsi Sulawesi Selatan

2021 ◽  
Vol 3 (2) ◽  
pp. 109
Author(s):  
Hisyam Ihsan ◽  
Wahidah Sanusi ◽  
Risna Ulfadwiyanti
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Unemployment Rate ◽  
Poisson Regression ◽  
Likelihood Estimation ◽  
Generalized Poisson ◽  
South Sulawesi ◽  
Working Age ◽  
Working Age Population ◽  
Generalized Poisson Regression

Abstrak. Penelitian ini membahas tentang pembentukan model Generalized Poisson Regression (GPR) dan penerapannya pada angka pengangguran bagi penduduk usia kerja di Provinsi Sulawesi Selatan. Jenis penelitian ini adalah penelitian terapan yang menggunakan model regresi nonlinear, yaitu model regresi Poisson dan model GPR. Variabel respon yang digunakan adalah jumlah angka pengangguran pada usia kerja yang termasuk angkatan kerja di Provinsi Sulawesi Selatan pada tahun 2017. Adapun variabel-variabel prediktor yang digunakan yaitu persentase angkatan kerja terhadap penduduk usia kerja, Indeks Pembangunan Manusia, persentase bekerja terhadap angkatan kerja, kepadatan penduduk, dan pertumbuhan ekonomi. Penelitian menggunakan metode Maximum Likelihood Estimation (MLE) untuk mengestimasikan parameter dan menghasilkan sebuah model GPR. Variabel prediktor yang memberikan pengaruh secara signifikan adalah Indeks Pembangunan Manusia dan  persentase bekerja terhadap angkatan kerja.Kata kunci: Angka Pengangguran, Regresi Poisson, Overdispersi, Generalized Poisson Regression, Maximum Likelihood Estimation  Abstract. This study discusses the formation of the Generalized Poisson Regression (GPR) model and its application to the unemployment rate for the working age population in South Sulawesi Province. This type of research is applied research that uses the Poisson regression model, namely Poisson regression and GPR models. The response variabel used is the total unemployment rate at working age which includes the workforce in South Sulawesi Province in 2017. The predictor variables used are the percentage of the workforce on the working age population, the Human Development Index, the percentage of work on the labor force, population density, and economic growth. This research uses the Maximum Likelihood Estimation (MLE) method to estimate parameters and produce a GPR model. The predictor variables which have a significant influence are the Human Development Index and the percentage of work on the labor force.Keywords: Unemployment Rate, Poisson Regression, Overdispersion, Generalized Poisson Regression, Maximum Likelihood Estimation

scholarly journals Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate generalized Poisson regression

2021 ◽  
Vol 880 (1) ◽  
pp. 012043
Author(s):  
Setyorini Indah Purwanti ◽  
Sutikno ◽  
Purhadi
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Poisson Regression ◽  
Temporal Heterogeneity ◽  
Test Statistic ◽  
Response Variable ◽  
Generalized Poisson ◽  
Numerical Iteration ◽  
Spatial And Temporal Heterogeneity ◽  
Generalized Poisson Regression

Abstract Poisson regression is used to model the data with the response variable in the form of count data. This modeling must meet the equidispersion assumption. That is, the average value is the same as the variance. However, this assumption is often violated. Violation of the equidispersion assumption in Poisson regression modeling will result in invalid conclusions. These violations are an overdispersion and an underdispersion of the response variable. Generalized Poisson Regression (GPR) is an alternative if there is a violation of the equidispersion assumption. If there are two correlated response variables, modeling will use the Bivariate Generalized Poisson Regression (BGPR). However, in the panel data with the observation unit in the form of an area, BGPR is not quite right because there is spatial and temporal heterogeneity in the data. Geographically and Temporally Weighted Bivariate Generalized Poisson Regression (GTWBGPR) is a method for modeling spatial and temporal heterogeneity data. GTWBGPR is a development of GWBGPR. In GTWBGPR, besides accommodating spatial effects, it also accommodates temporal effects. This research will discuss the parameter estimation and test statistics for the GTWBGPR model. Parameter estimation uses Maximum Likelihood Estimation (MLE), but the result is not closed-form, so it is solved by numerical iteration. The numerical iteration used is Newton-Raphson. The test statistic for simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT). With large samples, then this test statistic has a chi-square distribution approximation. So the test statistic for the partial test uses the Z test statistic.

scholarly journals Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

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