Estimasi Parameter Pada Model Poisson Point Process Berbasis Regresi Zero Inflated Poisson

Pratama, Jaka (2022) Estimasi Parameter Pada Model Poisson Point Process Berbasis Regresi Zero Inflated Poisson. Masters thesis, Institut Teknologi Sepuluh Nopember Surabaya.

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Abstract

Pada suatu Inhomogeneous Poisson Point Process (IPP), membentuk model regresi bagi fungsi intensitas merupakan salah satu tujuan utama dalam analisis spatial point process. Metode Berman-Turner Approximation diterapkan pada log-likelihood fungsi intensitas IPP sehingga log-likelihood tersebut akan ekivalen dengan log-likelihood regresi Poisson. Pendugaan parameter fungsi intensitas IPP selanjutnya dilakukan dengan menerapkan Maximum Likelihood Estimate (MLE) pada log-likelihood regresi Poisson. Pendugaan parameter berdasarkan metode berbasis regresi Poisson melibatkan banyak titik dummy untuk menurunkan error aproksimasi. Banyaknya titik dummy yang digunakan mengakibatkan banyak variabel respon bernilai 0 dan disebut dengan kondisi excess zeroes. Dalam pemodelan Generalized Linear Model (GLM), jika variabel respon memiliki excess zeroes, prediksi dengan model regresi Poisson menjadi tidak cukup baik lagi sehingga, beberapa literatur menyarankan pemodelan regresi Zero Inflated Poisson (ZIP) untuk pendugaan parameter. Penelitian ini memiliki sudut pandang yang berbeda dari penelitian-penelitian sebelumnya dalam pengembangan metode Berman-Turner Approximation. Penelitian ditujukan untuk meningkatkan kecocokan fungsi intensitas IPP dengan mengajukan pendekatan Berman-Turner berbasis regresi ZIP sebagai alternatif regresi Poisson. Pada studi simulasi, dilakukan estimasi parameter berdasarkan point pattern yang dibangkitkan dari regresi ZIP akan dibandingkan berdasarkan Standar Deviasi (SD), Bias dan Root of Mean Squared Error (RMSE) untuk berbagai perlakuan jumlah titik dummy. Hasil simulasi menunjukkan bahwa pada kondisi dummy pattern yang dibangkitkan yang lebih baik daripada metode berbasis regresi ZIP. Pada kondisi dummy pattern yang terkonsentrasi di sekitar titik data, metode berbasis regresi ZIP memiliki fungsi intensitas spesies pohon Beilschmiedia Pendula
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In an Inhomogeneous Poisson Point Process (IPP), forming a regression model for the intensity function is one of the main objectives in spatial point process analysis. The Berman-Turner Approximation method is applied to the log-likelihood of the IPP intensity function so that the log-likelihood will be equivalent to the log-likelihood of the Poisson regression. Estimation of the parameters of the IPP intensity function is then carried out by applying the Maximum Likelihood Estimate (MLE) on the log-likelihood Poisson regression. Parameter estimation based on the Poisson regression-based method involves many dummy points for reduce the approximation error. The number of dummy points used causes many response variables to be 0 and is called an excess zero condition. In the Generalized Linear Model (GLM) modeling, if the response variable has excess zeroes, the predictions with the Poisson regression model are no longer good enough, so some literature suggests Zero Inflated Poisson (ZIP) regression modeling for parameter estimation. This research has a different point of view from previous studies in developing the Berman-Turner Approximation method. The aim of this research is to improve the fit of the IPP intensity function by proposing a Berman-Turner approach based on ZIP regression as an alternative to Poisson regression. In the simulation study, parameter estimation based on point patterns generated from the ZIP regression will be compared based on Standard Deviation (SD), Bias and Root of Mean Squared Error (RMSE) for various treatments of the number of dummy points. The simulation results show that the generated dummy pattern is better than the ZIP regression-based method. In the condition of the dummy pattern concentrated around the data points, the ZIP regression-based method has the Beilschmiedia Pendula tree species intensity function

Item Type:	Thesis (Masters)
Additional Information:	RTSt 519.536 Jak e-1 2022
Uncontrolled Keywords:	Berman-Turner Approximation, Inhomogeneous Poisson Point Process, Regresi Zero Inflated Poisson; Berman-Turner Approximation, Inhomogeneous Poisson Point Process, Zero Inflated Poisson Regression
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	EKO BUDI RAHARJO
Date Deposited:	14 Apr 2023 03:16
Last Modified:	14 Apr 2023 03:16
URI:	http://repository.its.ac.id/id/eprint/97870

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