REGRESI SPLINES BENTUK-TERBATAS MONOTON (MONOTONE SHAPE-RESTRICTED REGRESSION SPLINES)

• Main Authors: , ESTRI PURWANI, , Drs. Zulaela, Dipl. Med. Stats., M.Si.
• Format: Theses and Dissertations NonPeerReviewed
• Published: [Yogyakarta] : Universitas Gadjah Mada 2013
• Subjects: ETD
• Online Access: https://repository.ugm.ac.id/124009/; http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=64127

Regression analysis is a statistical analysis that is often used to explore the relationship between predictor variable and response variable. If the assumption of a parametric form was known, parametric regression can be performed. But if the parametric form was not known, the estimated regression functions can be performed with nonparametric regression. Nonparametric regression method that is often preferred is regression splines because it uses less parameters in the estimation process. Regression splines can model the data that have different characteristics in the interval , . Estimation process is done by deviding , to be some sub intervals that have similar characteristics. Regression splines is known to be sensitive to number and location of knot so it need Generalized Cross-Validation to determine the optimal number and location of knot. In many practical settings, the predictor and response variable are known to preserve certain shape restrictions such as monotonicity. That monotonicity assumptions can be imposed on the regression splines estimation process, which is then called monotone shape-restricted regression splines. Estimate monotone shape-restricted function can be obtained using linear combination of I-splines basis functions and restrict the coefficients of these basis function to be positive. The restricted version have smaller mean squared error (MSE) and greater Rsquare than unrestricted version. In this paper, monotone shape-restricted regression splines is applied to analyze the relationship of age and toddler height in posyandu Sakura, Caturharjo village, Pandak subdistrict, Bantul regency. Then monotone shaperestricted regression splines estimation results are compared with regression splines and simple linear regression. By looking at the estimation results of the regression curve, MSE and R-square, it is concluded that monotone shaperestricted regression splines better than others.