Multivariate Zero-Inflated Poisson Inverse Gaussian Regression

Ermawati, Ermawati (2022) Multivariate Zero-Inflated Poisson Inverse Gaussian Regression. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model Zero-Inflated Poisson Inverse Gaussian Regression (ZIPIGR) dapat digunakan untuk menangani terjadinya overdispersi, yaitu data dengan nilai variansi lebih besar dari mean yang salah satu penyebabnya adalah terdapat banyak nilai nol (excess zero) pada respon, tetapi model ini hanya terbatas pada kasus univariat sehingga dalam penelitian ini dikembangkan suatu model regresi multivariate yaitu model Multivariate Zero-Inflated Poisson Inverse Gaussian Regression (MZIPIGR) tipe II. Penaksiran parameter dalam penelitian ini menggunakan metode Maximum Likelihood Estimation (MLE), tetapi turunan pertama dari fungsi ln likelihood diperoleh bentuk yang tidak closed form, sehingga proses penaksiran parameter dilanjutkan dengan iterasi Berndt-Hall-Hall-Hausman (BHHH). Penentuan statistik uji secara serentak menggunakan metode Maximum Likelihood Ratio Test (MLRT), sedangkan uji parsial menggunakan uji Wald. Dalam penelitian ini dilakukan studi simulasi pada perbandingan model BZIPIGR tipe II yang melibatkan dan tanpa variabel exposure yang menghasilkan model yang melibatkan variabel exposure lebih baik daripada model tanpa variabel exposure. Studi simulasi yang ke dua diperoleh bahwa model ZIPIGR lebih baik dalam menangani terjadinya kasus overdispersi daripada model regresi Poisson maupun model ZIPR. Penerapan model MZIPIGR selanjutnya dilakukan dengan melibatkan variabel exposure. Hasil penerapan model MZIPIGR tipe II pada kasus jumlah kematian ibu, neonatal, dan post neonatal di Provinsi Sulawesi Selatan Tahun 2018, diperoleh bahwa faktor yang berpengaruh signifikan terhadap jumlah kematian ibu adalah persentase kunjungan ibu hamil K4, persentase ibu hamil yang mendapatkan tablet Fe3, persentase persalinan oleh tenaga pesehatan, persentase kunjungan ibu nifas tiga kali, persentase posyandu aktif, dan persentase komplikasi obstetri di tangani. Sedangkan pada respon jumlah kematian neonatal tidak siginifikan dipengaruhi oleh persentase persalinan oleh tenaga pesehatan. Jumlah kematian post neonatal tidak signifikan dipengaruhi oleh persentase ibu hamil yang mendapatkan tablet Fe3 dan persentase komplikasi obstetri ditangani.
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The Zero-Inflated Poisson Inverse Gaussian Regression (ZIPIGR) model can be used to deal with overdispersion, namely data with a variance value larger than the mean, one of the causes of which is that there are many excess zeros in the response, but this model is only limited to univariate cases. Therefore, this studied was developed a multivariate regression model, namely the Multivariate ZeroInflated Poisson Inverse Gaussian Regression (MZIPIGR) type II model. The parameter estimation in this study uses the Maximum Likelihood Estimation (MLE) method. But the first derivative obtained for each parameter of the log likelihood function is in non-closed form, so the maximization process continues with numerical iteration, which uses the Berndt–Hall–Hall–Hausman (BHHH) algorithm. Determination of statistics simultaneously using the Maximum Likelihood Ratio Test (MLRT), while the partial test uses the Wald test. In this study, a simulation study was conducted on the BZIPIGR type II model involving and without exposure variables, which resulted in a model involving a variable that was better than the model without the exposure variable. The second simulation study has found that the ZIPIGR model is better at handling overdispersion cases than the Poisson regression model and the ZIPR model. The application of the MZIPIGR model is then carried out by involving the exposure variable. The results of the application of the MZIPIGR type II model in the case of the number of maternal, neonatal, and post-neonatal mortalities in South Sulawesi Province in 2018. The factors that significantly affect to the number of mortalities are on percentage of visits by pregnant women, pregnant women who received Fe tablets, deliveries by health workers, attended at least three postpartum maternal visits, active integrated service posts, and obstetric complications handled. While, the response to the number of neonatal deaths has not determined by the proportion of deliveries by health workers. The number of post-neonatal deaths was not significantly influenced by the percentage of pregnant women who received Fe tablets and obstetric complications that have been treat.

Item Type:	Thesis (Doctoral)
Additional Information:	RDSt 519.536 Erm m-1 2022
Uncontrolled Keywords:	BHHH, Excess Zero, Kematian Ibu, Neonatal, Post Neonatal, MLE, MZIPIGR Tipe II, Overdispersi, Excess Zero, Kematian Ibu
Subjects:	H Social Sciences > HA Statistics > HA31.35 Analysis of variance H Social Sciences > HA Statistics > HA31.3 Regression. Correlation. Logistic regression analysis.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Anis Wulandari
Date Deposited:	27 May 2024 07:51
Last Modified:	27 May 2024 07:51
URI:	http://repository.its.ac.id/id/eprint/107993

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