Model Multivariate Adaptive Regression Splines (MARS) Birespon Kontinu Dengan Pendekatan Fuzzy Clustering Means (FCM)

Meilisa, Mira (2024) Model Multivariate Adaptive Regression Splines (MARS) Birespon Kontinu Dengan Pendekatan Fuzzy Clustering Means (FCM). Doctoral thesis, Institut Teknologi Sepuluh Nopember.

	Text 7003201003-Disertasi.pdf - Accepted Version Restricted to Repository staff only until 1 October 2026. Download (4MB) | Request a copy
	Text 7003201003-Disertasi.pdf - Accepted Version Restricted to Repository staff only until 1 October 2026. Download (4MB) | Request a copy

Abstract

Pemodelan regresi seringkali tidak dapat diselesaikan dengan pendekatan regresi parametrik sehingga harus diselesaikan dengan pendekatan regresi nonparametrik. Pendekatan regresi nonparametrik digunakan apabila tidak terdapat informasi mengenai bentuk kurva dan tidak jelasnya pola hubungan antara variabel prediktor dengan variabel respon. Multivariate Adaptive Regression Splines (MARS) termasuk kedalam salah satu pendekatan regresi nonparametrik, merupakan kombinasi kompleks antara spline truncated dengan Recursive Partitioning Regression (RPR). Pemodelan MARS pada regresi bisa melibatkan respon kontinu dan respon kategori, baik pada satu respon maupun dua respon. Penelitian ini mengusulkan sebuah metode baru dalam perkembangan model MARS yang mengamati aspek heterogenitas yang tidak teramati. Metode ini merupakan kombinasi antara MARS birespon kontinu (MARSBK) dan Fuzzy Clustering Means (FCM) menjadi model Multivariate Adaptive Birespon Fuzzy Clustering Means Regression Splines (MABFCMRS) yang memungkinkan sebuah objek berada pada banyak cluster walaupun dengan bobot keanggotaan yang berbeda. Berbeda dengan pendekatan Fuzzy Clustering Means biasa yang menggunakan jarak Euclid sebagai bagian untuk penentuan bobot objek, metode baru yang diusulkan ini menggunakan total kuadrat jarak residual terboboti. Mendapatkan estimasi parameter menggunakan fungsi Lagrange Multiplier dan untuk menemukan banyaknya objek dalam cluster. Selanjutnya statistik uji kesamaan model menggunakan Sum Square Error (SSE), untuk pengujian hipotesis parameter model MABFCMRS secara serentak menggunakan Maximum Likelihood Ratio Test (MLRT) dan uji Wald untuk uji parsial. Kajian aplikasi dilakukan dengan menerapkan model MABFCMRS pada prevalansi stunting dan wasting menurut kecamatan di provinsi Sulawesi Tenggara. Hasilnya penelitian menunjukkan bahwa bayi dengan BBLR, bayi yang mendapat ASI ekslusif dan bayi mendapatkan vitamin A merupakan variabel signifikan yang berpengaruh pada prevalansi kasus stunting. Validasi indeks jumlah cluster terbaik berdasarkan kriteria Fuzziness Perfomance Index (FPI) dan Normalized Classification Entropy (NCE) adalah 2 cluster. Kriteria kebaikan model menggunakan nilai R Square dan Generalized Cross Validation (GCV) memperlihatkan model MABFCMRS lebih baik dari model MARSBK dalam memodelkan kasus prevalansi stunting dan wasting menurut kecamatan di Provinsi Sulawesi Tenggara.
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A parametric regression approach often cannot solve regression modeling, necessitating the use of a non-parametric approach. Researchers use the nonparametric regression approach when they lack information about the function form and encounter an unclear pattern of relationship between the predictor variable and the response variable. Multivariate Adaptive Regression Splines (MARS), included in one of the nonparametric regression approaches, is a complex combination of spline truncated and recursive partitioning regression. (RPR). MARS modeling on regression can involve continuous responses and category responses, both on one and two responses. This research proposes a new method for the development of the MARS model. The method combines MARS continuous response and fuzzy clustering means (FCM) into the Multivariate Adaptive Birespon Fuzzy Clustering Means Regression Splines (MABFCMRS) model. This model lets an object be in more than one cluster, even if the weights of those memberships are different. Unlike the usual fuzzy clustering means approach that uses Euclid distance as part of the determination of the object's weight, this new method proposed uses the total square of the residual clustering means generated by the MABFCMRS model. Obtain parameter estimates using the Lagrange Multiplier function and to find the number of objects in the cluster. Furthermore, the model similarity test statistics use Sum Square Error (SSE), using the maximum likelihood ratio test (MLRT) for simultaneously tested and partially with the Wald test. We conducted the application study by applying the MABFCMRS model to the prevalence of stunting and wasting in each sub-district of Southeast Sulawesi province. The results showed that LBW infants, exclusively breastfed infants, and vitamin A infants are significant variables that affect the prevalence of stunting cases. Validation of the best cluster number index based on Fuzziness Perfomance Index (FPI) and Normalized Classification Entropy (NCE) criteria is 2 clusters. Model goodness criteria using R Square and Generalized Cross Validation (GCV) values show that the MABFCMRS model is better than the MARSBK model in modeling the prevalence of stunting and wasting cases by sub-district in Southeast Sulawesi Province.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	MARSBK, FCM, MABFCMRS, Stunting, Wasting.
Subjects:	Q Science > Q Science (General) > Q325.5 Machine learning. Support vector machines.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Mira Meilisa
Date Deposited:	30 Aug 2024 01:47
Last Modified:	30 Aug 2024 01:47
URI:	http://repository.its.ac.id/id/eprint/115477

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