Sparse Group Lasso Untuk Estimasi Fungsi Intensitas Multivariate Poisson Point Process (Studi Kasus : Pemodelan Sebaran Pohon Di Pulau Barro Colorado)

Husain, Ahmad (2022) Sparse Group Lasso Untuk Estimasi Fungsi Intensitas Multivariate Poisson Point Process (Studi Kasus : Pemodelan Sebaran Pohon Di Pulau Barro Colorado). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Spatial point pattern merupakan sekumpulan titik yang mewakili lokasi kejadian atau benda dalan suatu wilayah tertentu. Penelitian ini terinspirasi dari data spesies pohon di Barro Colorado Island (BCI) yang telah banyak digunakan dalam penelitian spatial point process. Pada data tersebut, terdapat 297 spesies pohon dan 93 faktor lingkungan. Jika proses analisis menggunakan model Inhomogeneous Poisson Point Process (IPP) maka membutuhkan perulangan sesuai jumlah variat (spesies) sehingga asumsi keterkaiatan antar variat dihiraukan. Pada penelitian ini dikonstruksi model Inhomogeneous Multivariate Poisson Point Process (IMPP) yang dapat melakukan analisis secara simultan. Sebagai pendekatan model IMPP, digunakan pendekatan regresi Poisson dan logistik. Pemilihan model terbaik dari kedua pendekatan dilakukan dengan menyelidiki nilai Akaike information critetia (AIC), dummy point, dan waktu komputasi. Model terbaik selanjutnya ditambahkan metode regularisasi sparse group lasso (SGL). Metode regularisasi SGL bertujuan untuk menyeleksi variabel dengan mekanisme pengelompokan variabel prediktor. Berdasarkan hasil analisis, pemodelan sebaran sembilan spesies pohon di BCI, diketahui bahwa nilai AIC pendekatan regresi Poisson tidak menunjukkan perbedaan yang signifikan dengan pendekatan regresi logistik, sedangkan kriteria dummy point menunjukkan bahwa pendekatan regresi logistik hampir 10 kali lebih sedikit dibandingkan regresi Poisson mengakibatkan waktu komputasi lebih cepat 10 kali. Diperoleh bahwa pendekatan rergesi logistik adalah pendekatan yang terbaik. Hasil analisis diketahui bahwa variabel lingkungan seperti konvergensi, ketinggian, kandungan potasium, dan kandungan mineral nitrogen mayoritas berpengaruh secara signifikan terhadap keberadaan sembilan spesies pohon. Sejalan dengan metode SGL, untuk tuning parameter kedua α=0,8 diperoleh bahwa kemiringan wilayah, kandungan potassium, dan kandungan alumunium dianggap tidak berpengaruh terhadap keberadaan sembilan jenis spesies pohon di BCI.
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Spatial point pattern is a set of points that represent the location of events or objects in a certain area. This research was inspired by tree species data on Barro Colorado Island (BCI) which has been widely used in spatial point process research. In the data, there are 297 tree species and 93 environmental factors. If the analysis process uses the Inhomogeneous Poisson Point Process (IPP) model, it will require iteration according to the number of variates (species) so that the assumption of correlation between variables is ignored. In this study, the Inhomogeneous Multivariate Poisson Point Process (IMPP) model was constructed which can perform simultaneous analysis. As the IMPP model approach, Poisson regression and logistic approaches are used. The selection of the best model from the two approaches is done by investigating the Akaike information criteria (AIC), dummy point, and computation time. The best model is then added with the sparse group lasso (SGL) regularization method. The SGL regularization method aims to select variables using the predictor variable grouping mechanism. Based on the analysis results, modeling the distribution of nine tree species in BCI, it is known that the AIC value of the Poisson regression approach does not show a significant difference with the logistic regression approach, while the dummy point shows that the logistic regression approach is almost 10 times less than the Poisson regression, resulting in more computational time. fast 10 times. So it is known that the logistic regression approach is the best approach. The results of the analysis showed that environmental variables such as convergence, altitude, potassium content, and nitrogen mineral content had a significant effect on the existence of nine tree species. In line with the SGL method, for tuning the second parameter α=0,8, it was found that the slope of the area, potassium content, and aluminum content were considered to have no effect on the presence of nine tree species in BCI.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Barro Colorado Island, Inhomogeneous Multivariate Poisson point process, Regresi logistik, Regresi Poisson, Sparse group lasso
Subjects:	Q Science > QA Mathematics > QA274.2 Stochastic analysis
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Ahmad Husain
Date Deposited:	19 Feb 2022 21:11
Last Modified:	31 Oct 2022 03:44
URI:	http://repository.its.ac.id/id/eprint/94640

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