Penaksiran Parameter dan Pengujian Hipotesis pada Model Regresi Bivariate Zero-Inflated Negative Binomial

Azwarini, Rahmania (2023) Penaksiran Parameter dan Pengujian Hipotesis pada Model Regresi Bivariate Zero-Inflated Negative Binomial. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model statistika yang dapat digunakan untuk mengatasi under/overdispersi dan excess zero secara bersamaan pada data cacahan diantaranya adalah Bivariate Zero-Inflated Negative Binomial Regression (BZINBR). Model BZINBR memiliki kelebihan yaitu tidak mensyaratkan nilai varians yang sama dengan nilai rata-rata pada variabel respon, serta terdapat parameter dispersi yang berguna untuk menggambarkan variasi dari data. Model BZINBR dapat diterapkan pada data cacahan yang terdiri atas dua variabel respon. Penelitian ini berfokus pada penaksiran parameter model BZINBR tipe II menggunakan metode Maximum Likelihood Estimation (MLE) dengan iterasi numerik Berndt–Hall–Hall–Hausman (BHHH) serta pengujian hipotesis secara serentak dan parsial dengan menggunakan Maximum Likelihood Ratio Test (MLRT). Model BZINBR selanjutnya dikembangkan dan diaplikasikan untuk studi kasus pada data jumlah kematian ibu hamil dan jumlah kematian ibu nifas di Karesidenan Pekalongan Provinsi Jawa Tengah tahun 2017. Berdasarkan data diketahui bahwa persentase nilai nol pada data kematian ibu hamil yaitu sebesar 74,73% dan pada data kematian ibu nifas yaitu sebesar 65,93%. Persentase nilai nol yang berlebih dapat mengindikasikan adanya extra zeros serta terdapat pelanggaran asumsi equidispersi yaitu under/overdispersi. Hasil penelitian menunjukkan bahwa pemodelan BZINBR terbaik yaitu pemodelan dengan melibatkan variabel exposure. Selanjutnya melalui pengaplikasian model BZINBR terbaik didapatkan hasil bahwa seluruh variabel prediktor berpengaruh signifikan terhadap jumlah kematian ibu hamil dan jumlah kematian ibu nifas, selain itu diketahui pula parameter dispersi pada model BZINBR tipe II mampu menangani adanya overdispersi pada data jumlah kematian ibu hamil dan jumlah kematian ibu nifas di Karesidenan Pekalongan Provinsi Jawa Tengah.
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The statistics model that can be used to overcome under/overdispersion and excess zero simultaneously in count data is Bivariate Zero-Inflated Negative Binomial Regression (BZINBR). BZINBR model has the advantages that it does not require the same variance value as the average value of the response variables, and there is dispersion parameter to describe the variation of the data. BZINBR model can be applied to count data that consist of two response variables. This study focuses on the parameters estimation of the BZINBR type II model using the Maximum Likelihood Estimation (MLE) method with Berndt–Hall–Hall–Hausman (BHHH) numerical iterations and also simultaneous and partial hypothesis testing using the Maximum Likelihood Ratio Test (MLRT). The BZINBR model is then developed and applied to case studies on data about the number of pregnant women deaths and the number of postpartum maternal deaths in the Pekalongan Residency of Central Java Province in 2017. Based on the data,it is known that the percentage of zero values in the data about pregnant women deaths is 74.73% and in postpartum maternal deaths is 65.93%. Excess percentage of zeros can indicate extra zeros and there is a violation of the equidispersion assumption, namely under/overdispersion. The results showed that the best BZINBR modeling is the model with exposure variables. Furthermore, through the application of the best BZINBR model, it is found that all predictor variables has significant effects on the number of pregnant women deaths and the number of postpartum maternal deaths. In addition, it is also known that the dispersion parameter in the BZINBR type II model is able to handle overdispersion in data about the number of pregnant women deaths and the number of postpartum maternal deaths in the Pekalongan Residency, Central Java Province.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Bivariate Zero-Inflated Negative Binomial, BHHH, Extra Zeros, Kematian Ibu Hamil, Kematian Ibu Nifas, Postpartum Maternal Deaths, Pregnant Women Deaths
Subjects:	H Social Sciences > H Social Sciences (General) H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HA Statistics > HA31.7 Estimation Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression R Medicine > R Medicine (General) R Medicine > RA Public aspects of medicine R Medicine > RA Public aspects of medicine > RA971 Health services administration. R Medicine > RG Gynecology and obstetrics
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Rahmania Azwarini
Date Deposited:	07 Aug 2023 06:39
Last Modified:	07 Aug 2023 06:39
URI:	http://repository.its.ac.id/id/eprint/103154

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