Diantini, Ni Luh Sri (2022) Penaksiran Parameter dan Pengujian Hipotesis Model Geographically Weighted Log Normal Regression. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Log Normal Regression (LNR) merupakan pemodelan regresi dengan variabel respon mengikuti distribusi Lognormal. Pemodelan menggunakan LNR menghasilkan penaksir parameter yang bersifat global. Namun, karakteristik suatu wilayah dapat mempengaruhi model, apabila diabaikan akan menyebabkan non-stasioneritas spasial karena data yang digunakan memiliki varians yang tidak konsisten. Oleh karena itu, diperlukan pemodelan LNR yang mengakomodasi pengaruh spasial berupa koordinat lintang dan bujur yaitu Geographically Weighted Log Normal Regression (GWLNR), sehingga diperoleh penaksir parameter yang bersifat lokal untuk masing-masing lokasi pengamatan. Pada penelitian ini dibahas mengenai penaksiran parameter dan pengujian hipotesis model GWLNR. Pemodelan GWLNR diaplikasikan pada data Jumlah Penduduk Miskin Pulau Papua tahun 2019. Hasil penelitian menunjukkan bahwa penaksiran parameter menggunakan metode Maximum Likelihood Estimation (MLE) menghasilkan persamaan yang tidak closed form sehingga dilanjutkan dengan metode iterasi numerik Newton Raphson serta pengujian hipotesis menggunakan metode Maximum Likelihood Ratio Test (MLRT). Pengujian heterogenitas spasial menunjukkan adanya pengaruh spasial pada data. Nilai AICc model GWLNR lebih kecil dibandingkan dengan model LNR, sehingga disimpulkan bahwa model GWLNR lebih baik untuk memodelkan Jumlah Penduduk Miskin di Pulau Papua.
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Log Normal Regression (LNR) is a regression modeling to model the response variable that have the Lognormal distribution. The respons variable in LNR must be continuous and positive. In modeling using LNR, global parameters were obtained for all observation locations. However, the characteristics of a region can influence modeling, so that if this spatial influence is ignored it will produce spatial non-stationarity because the data used has inconsistent variances. Therefore, an approach is needed using Geographically Weighted Log Normal Regression (GWLNR). The GWLNR model will be applied to data on the Number of Poverty in Papua in 2019. This study aim to obtain parameter estimation and hypothesis testing of the GWLNR model and than obtain factors that influence the number of poverty in Papua in 2019 with GWLNR model. Parameter estimation is done using Maximum Likelihood Estimation (MLE) with the numerical iteration Newton Raphson. Hypothesis testing simultaneously uses the Maximum Likelihood Ratio Test method (MLRT), while for partial testing using wald test statistics. The results shows that the spatial heterogeneity testing is significant, it means the number of poverty in Papua depend on the geographical location. Based on AICc, GWLNR model is smallest than LNR model. Finally, we conclude that the GWLNR model was better than LNR to model the number of poverty in Papua in 2019.
| Item Type: | Thesis (Masters) |
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| Uncontrolled Keywords: | AICc, GWLNR, Kemiskinan, LNR, MLE, MLRT |
| Subjects: | Q Science > QA Mathematics > QA275 Theory of errors. Least squares. Including statistical inference. Error analysis (Mathematics) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Ni Luh Sri Diantini |
| Date Deposited: | 23 Feb 2022 20:51 |
| Last Modified: | 07 Oct 2024 02:38 |
| URI: | http://repository.its.ac.id/id/eprint/94729 |
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