Fathurahman, M. (2020) Geographically Weighted Multivariate Logistic Regression; Studi Kasus: Pemodelan Status Indeks Pembangunan Kesehatan Masyarakat dan Indeks Pembangunan Manusia Kabupaten/Kota di Pulau Kalimantan. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penelitian ini membahas model Multivariate Logistic Regression (MLR) dan model Geographically Weighted Multivariate Logistic Regression (GWMLR). MLR adalah model regresi yang dikembangkan dari distribusi multinomial. Model GWMLR adalah model MLR dengan semua parameter bergantung pada lokasi geografis, dan penaksiran parameter dilakukan secara lokal pada setiap lokasi pengamatan menggunakan pembobot spasial. Tujuan penelitian ini adalah mengembangkan model MLR dan GWMLR, yang meliputi penaksiran parameter dan pengujian hipotesis. Pengembangan model difokuskan untuk dua respon biner dan terdapat dependensi antar respon. Model MLR dan GWMLR yang telah dikembangkan diterapkan pada pemodelan status Indeks Pembangunan Kesehatan Masyarakat (IPKM) dan Indeks Pembangunan Manusia (IPM) kabupaten/kota di Pulau Kalimantan tahun 2018. Penaksiran parameter model menggunakan metode Maximum Likelihood Estimation (MLE) dan Metode Maximum Likelihood Ratio Test (MLRT) digunakan untuk pengujian hipotesis parameter model. Hasil penelitian menunjukkan bahwa penaksir maksimum likelihood parameter model berbentuk implisit. Penaksir maksimum likelihood dapat diperoleh dengan prosedur iteratif menggunakan metode Berndt-Hall-Hall-Hausman (BHHH). Statistik uji untuk pengujian hipotesis parameter secara asimtotik berdistribusi chi-square dan normal standar. Faktor-faktor yang berpengaruh terhadap status IPKM dan IPM kabupaten/kota di Pulau Kalimantan tahun 2018 adalah pertumbuhan ekonomi, Angka Partisipasi Murni (APM) Sekolah Menengah Pertama (SMP), persentase penduduk yang berpendidikan minimal SMP, rasio dokter per 1000 penduduk, dan jumlah puskesmas.
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This study discusses the Multivariate Logistic Regression (MLR) model and the Geographically Weighted Multivariate Logistic Regression (GWMLR) model. MLR is a regression model developed from a multinomial distribution. The GWMLR model is the MLR model with all parameters depending on geographic location, and parameter estimation is carried out locally at each observation location using spatial weighting. This study aims to develop the MLR and GWMLR models, which include parameter estimation and hypothesis testing. Model development is focused on two binary responses, and there are dependencies between responses. MLR and GWMLR models that have been developed are applied to modeling the status of the Public Health Development Index (PHDI) and Human Development Index (HDI) districts/cities in Kalimantan Island in 2018. The parameter estimation was done using the Maximum Likelihood Estimation (MLE) method, and the Maximum Likelihood Ratio Test (MLRT) method was used for hypothesis testing of model parameters. The results showed that the maximum likelihood estimator of the model parameters was an implicit form. The maximum likelihood estimator can be obtained by an iterative procedure using the Berndt-Hall-Hall-Hausman (BHHH) method. The test statistics for hypothesis testing of the parameters have an asymptotic chi-square and normal standard distributions. Factors influencing the status of PHDI and HDI of districts/cities in Kalimantan Island, in 2018 were economic growth, the Net Enrollment Rate of junior high schools, the percentage of the population who have the minimum level of education in junior high school, the ratio of doctors per 1000 population, and the number of public health center.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | regresi logistik multivariat, geographically weighted, maximum likelihood, BHHH, maximum likelihood ratio test, data spasial, IPKM, IPM. multivariate logistic regression, geographically weighted, maximum likelihood, BHHH, maximum likelihood ratio test, spatial data, PHDI, HDI. |
| Subjects: | H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics 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: | M. Fathurahman Fathurahman |
| Date Deposited: | 24 Aug 2020 07:21 |
| Last Modified: | 07 Jul 2023 16:12 |
| URI: | http://repository.its.ac.id/id/eprint/79095 |
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