Maharsi, Rengganis Woro (2023) Penaksiran Parameter Dan Pengujian Hipotesis Geographically Weighted Bivariate Poisson Log Normal Regression (Studi Kasus: Jumlah Komplikasi Kebidanan Dan Neonatal Provinsi Jawa Timur Tahun 2021). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Dua respon berupa data count dan mengalami overdispersi, berkorelasi positif, dan terdapat heterogenitas spasial, maka model regresi yang digunakan adalah Geographically Weighted Bivariate Poisson Log Normal Regression (GWBPLNR). Penelitian ini bertujuan mendapatkan estimasi parameter dan statistik uji pengujian hipotesis model GWBPLNR dengan dua variabel exposure dengan matriks pembobot menggunakan fungsi Gaussian kernel. Estimasi parameter GWBPLNR menggunakan MLE dengan iterasi numerik Berndt Hall Hall Hausman (BHHH) dan pengujian hipotesis menggunakan metode Maximum Likelihood Ratio Test (MLRT) pada taraf signifikansi 5%. Tujuan berikutnya memodelkan data jumlah komplikasi kebidanan dan neonatal kabupaten/kota di Provinsi Jawa Timur Tahun 2021. Pemilihan model terbaik berdasarkan nilai Akaike Information Criterion Corrected (AICc) yang terkecil. Turunan pertama fungsi ln likelihood model GWBPLNR terhadap parameter menghasilkan persamaan yang tidak closed form sehingga diselesaikan menggunakan iterasi BHHH. Pengujian kesamaan dengan statistik uji F hitung menghasilkan kesimpulan bahwa model GWBPLNR dan BPLNR berbeda. Pengujian serentak dengan statistik uji G2 yang berdistribusi Chi-Square dengan derajat bebas 2np berhasil menolak H0, artinya minimal terdapat satu variabel prediktor yang signifikan dalam model. Hasil pengujian parsial dengan statistik uji Z hitung dapat mengelompokkan kabupaten/kota di Provinsi Jawa Timur tahun 2021 berdasarkan variabel prediktor yang signifikan pada jumlah komplikasi kebidanan menjadi lima (5) kelompok dan terhadap jumlah komplikasi neonatal menjadi tiga (3) kelompok. Pengelompokan kabupaten/kota berdasarkan variabel yang signifikan secara bersama-sama terhadap kedua respon menghasilkan enam (6) kelompok. Berdasarkan nilai AICc, model terbaik adalah model GWBPLNR dengan dua variabel exposure dan fungsi pembobot Fixed Gaussian Kernel.
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Two responses in the form of count data that experience overdispersion, positive correlation, and spatial heterogeneity, the regression model that can be used is Geographically Weighted Bivariate Poisson Log Normal Regression (GWBPLNR). This study aims to obtain parameter estimation and test statistics for hypothesis testing in the GWBPLNR model. Parameter estimation in GWBPLNR uses Maximum Likelihood Estimation (MLE) with Berndt Hall Hall Hausman (BHHH) numerical iteration, and hypothesis testing is conducted using the Maximum Likelihood Ratio Test (MLRT) method at a significance level of alpha (5%). The next goal is to model the data on the number of maternal and neonatal complications in the regencies/cities of East Java Province in 2021. The selection of the best model is based on the smallest Akaike Information Criterion Corrected (AICc) value. The first derivative of the ln likelihood function of the GWBPLNR model respect to the parameter not available in a closed form, so it is solved using BHHH iteration. The equality test with the test statistics F is used to test the difference between the GWBPLNR and BPLNR models. The simultaneous test using the G² test statistic, which follows the Chi-Square distribution with degrees of freedom 2np, successfully rejects the null hypothesis, indicating that at least one predictor variable is significant in the model. The partial testing with the test statistic Z can classify the districts/cities of East Java Province in 2021 into five (5) groups based on the significant predictor variables for maternal complications, and three (3) groups for neonatal complications. The grouping of districts/cities based on the significant variables for both responses together results in six (6) groups. Based on the AICc value, the best model is the GWBPLNR model with two exposure variables and a Fixed Gaussian Kernel weighting function.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Fixed Gaussian Kernel, GWBPLNR, Heterogenitas Spasial, Korelasi Positif, Overdispersi. Fixed Gaussian Kernel, GWBPLNR, Spatial Heterogeneity, Positive Correlation, Overdispertion. |
| Subjects: | H Social Sciences > HA Statistics > HA30.6 Spatial analysis H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HA Statistics > HA31.38 Data envelopment analysis. H Social Sciences > HA Statistics > HA31.7 Estimation H Social Sciences > HQ The family. Marriage. Woman |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Rengganis Woro Maharsi |
| Date Deposited: | 27 Jul 2023 07:36 |
| Last Modified: | 27 Jul 2023 07:36 |
| URI: | http://repository.its.ac.id/id/eprint/99559 |
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