Berliana, Sarni Maniar (2022) Model Geographically Weighted Multivariate Generalized Poisson Regression Studi Kasus: Pemodelan Kematian Bayi, Anak, dan Ibu di Pulau Jawa). Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penelitian ini bertujuan untuk mengembangkan model multivariate generalized Poisson regression (MGPR) dengan memasukkan exposure dalam model dan kovariansi didefinisikan sebagai fungsi variabel bebas. Exposure digunakan untuk memperhitungkan ukuran populasi yang berbeda dari setiap unit lokasi supaya mencerminkan intensitas suatu kejadian yang diteliti, sedangkan pendefinisian kovariansi sebagai fungsi variabel bebas bertujuan untuk menghasilkan kovariansi yang lebih fleksibel. Model ini kemudian disebut sebagai model MGPR modifikasi. Selanjutnya, model MGPR modifikasi tersebut dikembangkan menjadi model geographically weighted multivariate generalized Poisson regression (GWMGPR) untuk memperhitungkan variasi spasial dalam memodelkan hubungan antara variabel bebas dengan variabel respon. Penaksiran parameter dilakukan dengan metode maximum likelihood estimation (MLE) dan diselesaikan dengan algoritma Newton-Raphson. Beberapa pengujian hipotesis parameter model MGPR modifikasi dan GWMGPR dilakukan dengan menggunakan metode likelihood ratio test (LRT). Model MGPR modifikasi dan GWMGPR diterapkan dengan menggunakan tiga variabel respon, disebut sebagai model trivariate generalized Poisson regression (TGPR) untuk meneliti faktor-faktor yang memengaruhi kematian kematian bayi, anak, dan ibu di Pulau Jawa dengan unit analisis kabupaten/kota. Ukuran exposure untuk jumlah kematian bayi, anak, dan ibu, masing-masing adalah jumlah kelahiran hidup, jumlah penduduk usia 1–4 tahun, dan jumlah wanita hamil. Model GWTGPR menghasilkan AICc sebesar 3.001,654, lebih kecil dari pada AICc model TGPR awal dan modifikasi, di mana masing-masing adalah 3.007,890 dan 3.007,893. Standard error penaksir parameter model TGPR modifikasi relatif lebih kecil dibandingkan dengan standard error penaksir model TGPR awal. Ini menunjukkan bahwa GWTGPR adalah model terbaik dan model TGPR modifikasi relatif lebih baik dari pada model TGPR awal.
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This study aims to develop a multivariate generalized Poisson regression (MGPR) model by including exposure in the model and the covariance is defined as a function of independent variables. Exposure is used to consider the different size of population of each location unit in order to reflect the intensity of an event being studied, while the definition of covariance as a function of independent variables is to produce a more flexible covariance. The model is then referred to as the modified MGPR model. Furthermore, the modified MGPR model was developed into a geographically weighted multivariate generalized Poisson regression (GWMGPR) model to take into account spatial variation in modelling the relationship between independent variables and response variables. The parameter estimation is carried out using the maximum likelihood estimation (MLE) method and solved by the Newton-Raphson algorithm. Several hypothesis testing of modified MGPR and GGMGPR model parameters were carried out by applying the likelihood ratio test (LRT) method. The modified MGPR and GWMGPR models are then applied using three response variables, called as trivariate generalized Poisson regression (TGPR) model to examine the factors that influence infant, child, and maternal mortality in Java with regency/municipality as analysis units. The measure of the exposures for the number of infant, child and maternal mortality are the number of live births, the number of population under five years old, and the number of pregnant women, respectively. The GWTGPR model yields an AICc of 3,001.654, which is smaller than the AICc of the original and modified TGPR models, which are 3,007.890 and 3,007.893, respectively. The standard error of the estimators of the modified TGPR model is relatively smaller than the standard error of the estimators of the TGPR model. This shows that GWTGPR is the best model and the modified TGPR model is relatively better than the original TGPR model.
| Item Type: | Thesis (Doctoral) |
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| Uncontrolled Keywords: | Geographically weighted regression, multivariate generalized Poisson regression, heterogenitas spasial, spatial heterogeneity, kesehatan ibu dan anak, maternal and child health |
| Subjects: | H Social Sciences > HA Statistics > HA30.6 Spatial analysis H Social Sciences > HA Statistics > HA31.7 Estimation Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | Sarni Maniar Berliana |
| Date Deposited: | 18 Feb 2022 10:21 |
| Last Modified: | 20 Aug 2024 07:25 |
| URI: | http://repository.its.ac.id/id/eprint/94409 |
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