Estimator Spline Dalam Regresi Nonparametrik Birespon Untuk Data Longitudinal (Studi Kasus Pada Pasien Penderita TB Paru Di Malang)

Fernandes, Adji Achmad Rinaldo (2016) Estimator Spline Dalam Regresi Nonparametrik Birespon Untuk Data Longitudinal (Studi Kasus Pada Pasien Penderita TB Paru Di Malang). Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

single response model approach for longitudinal data, or multi-responses model approach for cross section data. This study will be developed spline estimators in biresponses nonparametric regression for longitudinal data which accommodates correlation between observations of the same subject, and correlation between each responses. Initial study focused on the spline estimators form development and optimum smoothing parameters to estimate biresponses nonparametric regression curve in longitudinal data. In the final section, the result of theoretical study was applied on aplication data of Pulmonary Tuberculosis in Outpatient Ward of Pulmonary Policlinic and Inpatient of RSSA Malang in 2011 and simulation data. Biresponses nonparametric regression model which involved p predictors in longitudinal data, the estimators was expressed as follows: f (x)  *d*  *c*    T V . While spline estimators which met the criteria of minimizing Penalized Weighted Least Square (PWLS):         2 1 T 1 2 2 W [ , ], 1,2; 1,2,..., ; 1,2,..., 1 1 1 min ki ki m ki ki ki N p b m f a b k p i N ki ki it it k i a M y f  y f  f x dx                      Σ                 were fˆ *dˆ* *cˆ* * y    T  V  A      , with     * * *T ˆ 1 ˆ 1 * 1 *T ˆ 1 ˆ 1 * ˆ 1 ˆ[ * *T ˆ 1 ˆ * 1 *T ˆ 1 ˆ ]           A  T T U Σ T T U Σ  V U Σ IT T U ΣT T U Σ  . Optimum smoothing parameters opt  (11(opt),12(opt),...,2N(opt))  for biresponses nonparametric regression spline estimators in longitudinal data was obtained by minimizing function of GCV. Application on simulation data showed that: 1) Characteristics of exponential and trigonometric function of experiment yielded the highest level of accuracy, 2) the application of spline estimator of biresponses give the less efective in correlation level  between 0.1-0.3. The use of variancecovariances matrix of random error which accomodate the correlation between each responses usefullness in condition of correlation level  > 0.3. The higher level of correlation, the higher the R2 level obtained. The application on real data showed that the result of biresponses nonparametric spline estimators for longitudinal data on patients application data with Pulmonary TB had adequate level of prediction (82.8%).

Item Type: Thesis (Doctoral)
Additional Information: RDSt 519.536 Fer e
Uncontrolled Keywords: Estimator Spline, Birespon, Longitudinal, PWLS
Subjects: Q Science > QA Mathematics > QA278.2 Regression Analysis
Divisions: Faculty of Mathematics and Science > Statistics > 49001-(S3) PhD Thesis
Depositing User: ansi aflacha
Date Deposited: 09 Apr 2019 08:54
Last Modified: 09 Apr 2019 08:54
URI: https://repository.its.ac.id/id/eprint/62724

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