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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika)
Rohma, Usriatur
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Comparison of Nonparametric Path Analysis and Biresponse Regression using Truncated Spline Approach Azizah, Laila Nur; Rohma, Usriatur; Fernandes, Adji Achmad Rinaldo; Wardhani, Ni Wayan Surya; Astutik, Suci
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26739

Abstract

Nonparametric path analysis and biresponse nonparametric regression are two flexible statistical approaches to analyze the relationship between variables without assuming a certain form of relationship. This study compares the performance of the two methods with the truncated spline approach, which has the advantage of determining the shape of the regression curve through optimal selection of knot points. This study aims to evaluate the best model based on linear and quadratic polynomial degree with 1, 2, and 3 knot points. The model is applied to data with 100 samples and simulated data of various sample levels. The results show that the best model in nonparametric path analysis is a quadratic model with three knots, while the best model in biresponse nonparametric regression is a quadratic model with two knots. Biresponse nonparametric regression has a coefficient of determination of 88.8% which is higher than the nonparametric path analysis of 70.9%. The best biresponse nonparametric regression model is the model with quadratic order and two knots.
DEVELOPMENT OF NONPARAMETRIC PATH FUNCTION USING HYBRID TRUNCATED SPLINE AND KERNEL FOR MODELING WASTE-TO-ECONOMIC VALUE BEHAVIOR Rohma, Usriatur; Fernandes, Adji Achmad Rinaldo; Astutik, Suci; Solimun, Solimun
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp331-344

Abstract

Waste management remains a challenge, including in Batu City, East Java, Indonesia. Rapid population growth and economic activities in the city have resulted in a substantial increase in waste volume. One of the key factors in solving waste problems is the mindset of the community towards waste management. The application of statistical analysis methods can be an effective approach to solving problems related to waste management from an economic point of view. Nonparametric path analysis is a statistical method that does not rely on the assumption that the curve is known. Nonparametric path analysis is performed if the data does not fulfill the linearity assumption. This study aims to determine the best nonparametric path function with a hybrid truncated spline and kernel approach among EV values of 0.5; 0.8; and 1. In addition, this study also aims to test the significance of the best path function obtained. The data used in this study are timer data obtained from the Featured Basic Research Grant. The results showed that the best model of hybrid truncated spline and kernel nonparametric path analysis is a hybrid model of truncated spline nonparametric path of linear polynomial degree 1 knot and kernel triangle nonparametric path at EV 0.5. In addition, the significance of the best nonparametric truncated spline and kernel hybrid path function estimation using jackknife resampling shows that all exogenous variables have a significant effect on endogenous variables as evidenced by a p-value smaller than (0.05).
A Combined Truncated Spline and Kernel Semiparametric Path Model Development Rohma, Usriatur; Fernandes, Adji Achmad Rinaldo; Astutik, Suci; Solimun, Solimun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29849

Abstract

Semiparametric path analysis is a combination of parametric and nonparametric path analysis performed when the linearity assumption in some relationships is not met. In this study, the development of semiparametric path function estimation was carried out by combining two truncated spline and kernel approaches. In addition, the purpose of this study is to determine the significance of function estimation using t-test statistics at the jackknife resampling stage. This research was conducted in 135 Junrejo sub-districts of Batu district.  The results showed that the development of a combined semiparametric path function estimation of truncated spline and kernel with weighted least square allows a more flexible and accurate estimation in modeling waste management behavior patterns. 2. The significance of the best truncated spline nonparametric path estimation in the model of the effect of Environmental Quality and the Use of Waste Banks on the Economic Benefits of Waste through the Use of the 3R Principles using t test statistics at the jackknife resampling stage shows that all exogenous variables have a significant effect on endogenous variables.
Co-Authors Azizah, Laila Nur Fernandes, Adji Achmad Rinaldo Ni Wayan Surya Wardhani Solimun, Solimun Suci Astutik