Penaksiran Parameter dan Pengujian Hipotesis pada Model Geographically Weighted Multivariate Poisson Inverse Gaussian Regression

Mardalena, Selvi (2022) Penaksiran Parameter dan Pengujian Hipotesis pada Model Geographically Weighted Multivariate Poisson Inverse Gaussian Regression. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Tujuan dari penelitian ini adalah mengembangkan model regresi mixed Poisson untuk menangani kasus overdispersi pada data cacahan, yaitu model Multivariate Poisson Inverse Gaussian Regression (MPIGR) yang melibatkan variabel eksposur dan lebih dari dua variabel respon. Selanjutnya, model MPIGR dikembangkan menjadi model Geographically Weighted Multivariate Poisson Inverse Gaussian Regression (GWMPIGR) dengan memasukkan efek lokasi pada model. Kajian teori dilakukan untuk mendapatkan penaksir parameter model MPIGR dan GWMPIGR menggunakan metode Maximum Likelihood Estimation (MLE) dengan iterasi Newton-Raphson. Selanjutnya, statistik uji untuk pengujian hipotesis parameter model MPIGR dan GWMPIGR ditentukan menggunakan metode Maximum Likelihood Ratio Test (MLRT). Studi simulasi dilakukan untuk mengevaluasi turunan, program, dan kebaikan penaksiran parameter model MPIGR. Hasil studi simulasi menunjukkan bahwa turunan dan program penaksiran parameter model MPIGR sudah benar dan baik dalam menangani overdispersi yang tinggi. Selanjutnya, model MPIGR dan GWMPIGR digunakan untuk menentukan faktor yang mempengaruhi kematian bayi, anak balita, dan ibu di Jawa pada tahun 2019. Hasil penelitian menunjukkan bahwa pada model MPIGR, semua prediktor yaitu persentase posyandu aktif, persentase peserta aktif KB, persentase penduduk yang memiliki asuransi BPJS kesehatan, indeks Pendidikan, dan persentase rumah tangga yang memiliki sanitasi layak, signifikan berpengaruh terhadap jumlah kematian bayi, anak balita dan ibu di Jawa. Selanjutnya, model GWMPIGR dengan fungsi pembobot kernel fixed Gaussian dan kernel fixed bisquare menghasilkan beberapa kelompok wilayah berdasarkan variabel prediktor yang signifikan mempengaruhi jumlah kematian bayi, anak balita, dan ibu di Jawa pada tahun 2019. Berdasarkan nilai AICc, model GWMPIGR dengan fungsi pembobot kernel fixed bisquare lebih baik dari model MPIGR dan model GWMPIGR dengan fungsi pembobot kernel fixed Gaussian dalam memodelkan data jumlah kematian bayi, anak balita dan ibu di Jawa pada Tahun 2019.
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The purpose of this study is to develop a mixed Poisson regression model to deal with overdispersion in the count data, namely, a Multivariate Poisson Inverse Gaussian Regression (MPIGR) model involving eksposur variables and more than two response variables. Furthermore, the MPIGR model was developed into the Geographically Weighted Multivariate Poisson Inverse Gaussian Regression (GWMPIGR) model by including location effects in the model. Theoretical studies were conducted to obtain parameter estimators of the MPIGR and GWMPIGR models using the Maximum Likelihood Estimation (MLE) method with Newton-Raphson iterations method. The statistical test for hypothesis testing of the MPIGR and the GWMPIGR models were determined by using the Maximum Likelihood Ratio Test (MLRT) method. Simulation studies were conducted to evaluate the derivatives, program, and parameter estimation of the MPIGR model. The result of simulation study shows that the derivatives and the program of the MPIGR model is correct and good to deal with high overdispersion. Furthermore, the MPIGR and GWMPIGR models will be applied to determine the factors that affect the number of infant deaths, the number of under-five deaths, and the number of maternal deaths in Java in 2019. The results showed that in the MPIGR model, all predictor variables, namely the percentage of active integrated service post, the percentage of active family planning participants, the percentage of the population with BPJS health insurance, education index, and the percentage of household that has improved sanitation, had a significant effect on the number of infant, under-five, and maternal deaths in Java in 2019. The GWMPIGR model with Gaussian fixed kernel and bisquare fixed kernel weighting functions produce several regional groups based on significant variables that significantly affect the number of infant, under-five, and maternal deaths in Java in 2019. Based on the AICc value, the GWMPIGR model with a bisquare fixed kernel weighting function is better than the MPIGR model and the GWMPIGR model with a Gaussian fixed kernel weighting function in modeling data on the number of infant, under-5, and maternal deaths in Java in 2019.

Item Type:	Thesis (Doctoral)
Additional Information:	RDSt 519.536 Mar p-1
Uncontrolled Keywords:	GWMPIGR; Jumlah kematian bayi, anak balita, dan kematian ibu; MLE; MPIGR; Overdispersi, Overdispersion; The number of infants, under-5, and maternal deaths.
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	- Davi Wah
Date Deposited:	17 Apr 2023 07:43
Last Modified:	17 Apr 2023 07:43
URI:	http://repository.its.ac.id/id/eprint/97879

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