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.

Preview |
Text
1311301001-Disertation.pdf - Published Version Download (16MB) | Preview |

## 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 IT 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. Logistic regression |

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: | http://repository.its.ac.id/id/eprint/62724 |

## Actions (login required)

View Item |