Analisis Ridge Robust Penduga Generalized M (GM) Pada Pemodelan Kalibrasi Untuk Kadar Gula Darah
Keywords:
Adjusted Boxplot, Generalized M, Pemodelan kalibrasi, Ridge Robust
Abstract
Calibration modeling is one of the methods used to analyze the relationship between different methods. The relationship is like the relationship between invasive and non-invasive blood sugar measurement. Problems that often arise in calibration modeling are multicollinearity and outliers. Multicollinearity problems can cause the regression confidence interval to widen, so that there is no statistically significant regression coefficient. Outliers cause statistical tests to deviate. The handling of these problems can be solved by robust ridge analysis. Ridge robust is a combined analysis of ridge regression and robust regression. Ridge regression is able to overcome the problem of multicollinearity and robust regression can overcome the problem of outliers. The estimator used is Generalized M (GM). This method will be applied to a calibration model that uses invasive and non-invasive blood sugar level data. The model used with Generalized M (GM) estimator robust regression using modulation clusters 50 to 90 in 2017 is better than the modulation group 50. up to 90 in 2019. The statistical values obtained are SSE of 0.910, RMSEadj of 0.114, and RMSEP of 0.030. Calibration models that have outliers and multicollinearity problems can be overcome by robust ridge regression. The feasibility value of the model obtained in the GM estimator robust regression is smaller than the MM estimator ridge robust regression in the calibration modeling for non-invasive blood sugar level data. That is, the best model that can be used is the robust ridge regression GM estimator.
References
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Rousseeuw PJ, Leroy AM. 1987. Robust Regression and Outlier Detection. New York (US): John Willey and Sons.
Ryan TP. 1997. Modern Regression Methods. New York (US): John Wiley And Sons. Inc.
Said AZ, Fitrianto A, Erfiani. 2022. Pendeteksian pencilan pada data berdistribusi miring univariat menggunakan pendekatan modifikasi sequential fences. [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Samkar H, Alpu O. 2010. Ridge regression based on some robust estimators. Journal of Modern Applied Statistical Methods. 9(2): 495-501.
Satria E, Wildian. 2013. Rancangn bangun alat ukur kadar gula darah non-invasif berbasis mikrokontroler AT89S51 dengan mengukur tingkat kekeruhan spesimen urine menggunakan sensor fotodioda. Jurnal Fisika UNAND. 2(1): 40-47.
Schwertman NC, Silva RD. 2007. Identifying outliers with sequential fences. Computional Statistics and Data Analysis. 51(8) : 3800-3810.
Susanti Y, Liana T, Pratiwi H, Sulistijowati SH. 2014. M estimation, S estimation dam MM estimation in robust regression. International Journal of Pure and Applied Mathematics. 3(91): 349-360.
Tiro MA, Ahsan M. 2015. Penyajian Informatif : Tabel, Grafik, dan Statistik. Makassar (ID): Andira Publisher.
Wahyono T. 2004. Sistem Informasi. Yogyakarta: Graha Ilmu.
Wilcox RR. 2005. Introduction to Robust Estimation and Hypothesis. San Diego: Academic Press.
Wong HS, Fitrianto A. 2019. Adjusted sequential fences for detecting uniovariate outliers in skewed distribution. ASM Science Journal, 12(5): 107-115.
Yohai VJ. 1987. High breakdown-point and high-efficiency robust estimates for regression. The Annals of Statistics. 150(20): 642-656.
Avan. 2017. Pendugaan konsentrasi glukosa darah menggunakan jaringan syaraf tiruan pada alat non-invasive. [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Bowley AL. 1920. Elements of Statistics. Ed ke-4. London (UK): P.S. King & Son, ltd.
Brys G, Hubert M, Struyf A. 2004. A robust measure of skewness. Journal of Computational and Graphical Statistics. 13(4): 996-1017.
Chandraningtyas S, Safitri D, Ispriyanti D. 2013. Regresi robust MM-estimator untuk penanganan pencilan pada regresi linier berganda. Jurnal Gaussian. 2(4): 395-404.
Chen C. 2002. Robust regression and outlier detection with the ROBUSTREG procedure. Statistics and Data Analysis. SUGI Paper 265-27. North Carolina: SAS Institute.
Cousineau D, Chartier S. 2010. Outlier detection and treatment : a review. International Journal of Psychological Research. 3(1): 59-68
Daoud IJ. 2017. Multicolinierity and regression analysis. Journal of Physics: Conference Series 949.
Dereny M, Rashwan NI. 2011. Solving multicolinierity problem using ridge regression model. International Journal Contemporary Mathematical Sciences. 6(12): 585-600.
Gujarati DN. 2003. Basic Econometrics. Ed ke-4. New York (NY) : McGraw-Hill Companies, Inc.
Gujarati DN, Porter D. 2009. Basic Econometrics . Ed ke-5. New York (NY) : McGraw-Hill/Irwin.
Hair JF, Black WC, Babin BJ, Anderson RE. 2014. Multivariate Data Analysis. Ed ke-7. Edinburgh Gate (UK): Pearson.
Herianti. 2020. Pemodelan kalibrasi kekar (pengukuran glukosa darah non-invasif). [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Hruschka WR. 1987. Data analysis : wavelength selection methods. American of Association of Cereal Chemists. 35-55.
Huber PJ. 1981. Robust Statistics. New York (NY): John Wiley And Sons. Inc.
Huber PJ, Ronchetti EM. 2009. Robust Statistics. New York (NY): John Wiley And Sons. Inc.
Hubert M, Vandervieren E. 2008. An adjusted boxplot for skewed distribution. Computational Statistics and Data Analysis. 52: 5186 – 5201.
Ismah, Wigena AH, Djuraidah A. 2009. Pendekatan regresi kuadrat terkecil partial robust dalam model kalibrasi. Forum Statistika dan Komputasi. 14(1): 34-41.
Jayanti PGK, Anisa R, Aidi MN, Erfiani. 2018. Penerapan teknik prapemrosesan smoothing spline pada data hasil pengukuran alat pemantau glukosa darah non-invasif. Jurnal Xplore. 2(2): 15-35.
Jolliffe IT. 2002. Principal Component Analysis. Ed ke-2. New York (NY): Springer-Verlag.
Kim T, White H. 2004. On more robust estimation of skewness and kurtosis: simulation and application to the S & P500 indeks. Finance Research Letters. 1(1): 56-73.
Kutner MH, Nachtsheim CJ, John N, Li WG. 2005. Applied Linier Statistics Model. Ed ke-5. New York (US): Mc-Grawhill.
Lin TI, Lee JC, Hsieh WJ. 2007. Robust mixture modeling using the skew t-distribution. Statistics and Computing. 17(2): 81-92.
Mardikyan S, Cetin E. 2008. Efficient choice of biasing constant for ridge regression. International Journal Contemporary Mathematical Sciences. 3(11): 527-536.
Montgomery DC, Peck EA. 2012. Introduction to Linear Regression Analysis. Ed ke-5. New York (US): John Willey and Sons.
Naes T, Issakson T, Fearn T, Davies T. 2002. Multivariate Calibration and Classification. United Kingdom (GB): NIR Publications Chichester.
Nalwan A. 2004. Pengolahan Gambar Secara Digital. Jakarta (ID): PT Elex Media Komputindo.
Nugroho AB, Rintyarna BS, Athoillah DK. 2021. Analisis spektrum tegangan pada alat pendeteksi kadar gula darah menggunakan near. Jurnal Teknik Elektro dan Komputasi (ELKOM). 3(1): 1-13.
Nurdin N, Raupong, Islamiyati A. 2014. Penggunaan regresi robust pada data yang mengandung pencilan dengan metode momen. Jurnal Matematika, Statistika, dan Komputasi. 10(2): 114-123.
Pambudi N. 2012. Tingkat efisiensi estimasi-M terhadap estimasi-GM dalam regresi robust. [skripsi]. Surakarta (ID): Universitas Sebelas Maret Surakarta.
Peck R, Devore JL. 2012. The Exploration and Analysis of Data. Ed ke-7. Boston (USA): Brooks.
Rassiyanti L. 2020. Analisis regresi ridge robust pada pengukuran kadar glukosa darah non-invasif. [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Rosni. 2019. Pendekatan regresi komponen utama dan regresi kuadrat terkecil parsial untuk menduga kadar glukosa darah non-invasif. [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Rousseeuw PJ, Leroy AM. 1987. Robust Regression and Outlier Detection. New York (US): John Willey and Sons.
Ryan TP. 1997. Modern Regression Methods. New York (US): John Wiley And Sons. Inc.
Said AZ, Fitrianto A, Erfiani. 2022. Pendeteksian pencilan pada data berdistribusi miring univariat menggunakan pendekatan modifikasi sequential fences. [tesis]. Bogor (ID): Sekolah Pascasarjana IPB.
Samkar H, Alpu O. 2010. Ridge regression based on some robust estimators. Journal of Modern Applied Statistical Methods. 9(2): 495-501.
Satria E, Wildian. 2013. Rancangn bangun alat ukur kadar gula darah non-invasif berbasis mikrokontroler AT89S51 dengan mengukur tingkat kekeruhan spesimen urine menggunakan sensor fotodioda. Jurnal Fisika UNAND. 2(1): 40-47.
Schwertman NC, Silva RD. 2007. Identifying outliers with sequential fences. Computional Statistics and Data Analysis. 51(8) : 3800-3810.
Susanti Y, Liana T, Pratiwi H, Sulistijowati SH. 2014. M estimation, S estimation dam MM estimation in robust regression. International Journal of Pure and Applied Mathematics. 3(91): 349-360.
Tiro MA, Ahsan M. 2015. Penyajian Informatif : Tabel, Grafik, dan Statistik. Makassar (ID): Andira Publisher.
Wahyono T. 2004. Sistem Informasi. Yogyakarta: Graha Ilmu.
Wilcox RR. 2005. Introduction to Robust Estimation and Hypothesis. San Diego: Academic Press.
Wong HS, Fitrianto A. 2019. Adjusted sequential fences for detecting uniovariate outliers in skewed distribution. ASM Science Journal, 12(5): 107-115.
Yohai VJ. 1987. High breakdown-point and high-efficiency robust estimates for regression. The Annals of Statistics. 150(20): 642-656.
Published
2022-12-06
How to Cite
Agung Tri Utomo, Erfiani, E., & Fitrianto, A. (2022). Analisis Ridge Robust Penduga Generalized M (GM) Pada Pemodelan Kalibrasi Untuk Kadar Gula Darah. VARIANSI: Journal of Statistics and Its Application on Teaching and Research, 4(2), 59-69. https://doi.org/10.35580/variansiunm14
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