PERBANDINGAN METODE CROSS VALIDATION DAN GENERALIZED CROSS VALIDATION DALAM REGRESI NONPARAMETRIK BIRESPON SPLINE
Abstract
Regression analysis is one of the most popular methods in statistics to explain causal relationships between one predictor variables to one response variable. In general, modeling can be done using regression analysis. The regression curve can be assumed by the parametric regression approach and the nonparametric regression approach. However, not all data acquired follows a certain pattern so that this type of data uses a nonparametric regression approach. The nonparametric regression approach is not related to the assumption of the regression curve form as it is to the parametric regression, and more flexible. There are several techniques performed for estimation in nonparametric regression ie Spline. Some cases in the regression analysis found many problems that can not be solved by simple regression analysis of one response because if using two response variables in the research, it must be seen the value of correlation between variables. As a result, regression issues must be solved by the birespon regression model. This study aims to describe the IMR and malnutrition status of children under five and to get the Spline model in the best birespon nonparametric regression through the relationship between the suspected variables by using Cross Validation (CV) and Generalized Cross Validation (GCV) methods. The results obtained are the best model that is suitable for health by using CV method, obtained the minimum CV value located on Spline model linear one knot that is equal to 77.37831 with MSE of 76.75449.
References
[2] Depkes RI (Departemen Kesehatan RI). (2003). Indikator Indonesia Sehat 2010 dan Pedoman Penetapan Indikator Provinsi Sehat dan Kabupaten/Kota Sehat: Keputusan Menteri Kesehatan Nomor 1202/Menkes/SK/VIII/2003. Departemen Kesehatan RI, Jakarta.
[3] Budiantara, I. N. (2007). Pendugaan Model Fertilitas Wanita di Indonesia dengan Menggunakan Regresi Spline, Laporan Akhir Pelaksanaan Penelitian Studi Kajian Wanita Tahun Anggaran 2007, LPPM, Intitut Teknologi Sepuluh Nopember, Surabaya
[4] Budiantara, I. N. (2009). Spline dalam Regresi Nonparametrik dan Semiparametrik: Sebuah Pemodelan Statistika Masa Kini dan Masa Mendatang, ITS Press, Institut Teknologi Sepuluh Nopember Surabaya.
[5] Tripena, Agustini. (2011). Penentuan Model Regresi Spline Terbaik, Prosiding Seminar Nasional Statistika Universitas Diponegoro 2011, Semarang.
[6] Budiantara, I. N. (2000). Metode U, GML, CV dan GCV dalam Regresi Nonparametrik Spline, Majalah Ilmiah Himpunan Matematika Indonesia (MIHMI), 6, 41-45.
[7] Wang, Y. (1998). “Spline Smoothing Models with Correlated Error”. Journal of the Royal Statistical Sociaty, Series B, 5r0, 341-348.
[8] Craven, P., and Wahba, G. (1979). "Smoothing Noisy Data With Spline Functions". Numerische Mathematik, 31, 377-403
[9] Wahba, G. (1990). “Spline Model for Observational Data}”. SIAM, XII, Philadelphia.
[10] Eubank, R. L. (1988). “Spline Smoothing and Nonparametric Regression”. New York: Marcel Dekker.
[11] Fitriyani, Nurul. (2014). Metode Cross Validation Dan Generalized Cross Validation Dalam Regresi Nonparametrik Spline Studi Kasus Data Fertilitas Di Jawa Timur. Tesis, Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh Nopember (ITS), Surabaya
[12] Kemenkes Sumut (Kementerian Kesehatan Pemerintahan Provinsi Sumatera Barat). (2014). Profil Kesehatan Provinsi Sumatera Barat 2014. Sumatera Barat: Kementerian Kesehatan Pemerintahan Provinsi Sumatera Barat.
[13] Dinkes Jateng (Dinas Kesehatan Provinsi Jawa Tengah). (2015). Profil Kesehatan Provinsi Jawa Tengah Tahun 2015. Jawa Tengah: Pemerintah Provinsi Jawa Tengah.
[14] Santoso, Soegoeng dan Anne Lies Ranti. (2009). Kesehatan dan Gizi, Jakarta, Rineka Cipta
[15] Aulia, Annisya (2017). Faktor-faktor yang Mempengaruhi Derajat Kesehatan dengan Menggunakan Regresi Multivariat (Studi kasus : Derajat Kesehatan Kabupaten dan Kota di Provinsi Sumatera Barat). Diploma thesis, Universitas Andalas.
[16] Wulandari, I. D. A. M. I. (2014). Analisis Faktor – Faktor Yang Mempengaruhi Persentase Penduduk Miskin Dan Pengeluaran Perkapita Makanan Di Jawa Timur Dengan Metode Regresi Nonparametrik Birespon Spline. Tugas Akhir, Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh Nopember (ITS), Surabaya.
[17] Setyawan, N.A.D. (2011). Pendekatan Regresi Nonparametrik Birespon Spline untuk Pemodelan Determinan Tingkat Pendidikan di Pulau Papua, Thesis, Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh Nopember, Surabaya.
[18] Eubank, R. L. (1999). “Nonparametric Regression and Spline Smoothing Second Edition”. New York: Marcel Dekker.
[19] Budiantara, I. N. (2004). Model Spline Multivariabel dalam Regresi Nonparametrik, Makalah Seminar Nasional Matematika, Jurusan Matematika ITS Surabaya.
[20] Similia,T. Dan Tikka, J. (2007). Input Selection and Shrinkage in Multiresponse Linear Regression, Preprint Submitted to Elsevier.
[21] Draper, N.R. and Smith, H. (1998). “Applied Regression Analysis,Three Edition”. John Wiley and sons, Inc. New York.
[22] Andrews, Y. Ng. (1991). “Preventing “Overfitting” of Cross-Validation Data”.School of Computer Science, Carnegie Mellon University, Pittsburgh PA.
