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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Zero : Jurnal Sains, Matematika, dan Terapan
Adji Achmad Rinaldo Fernandes
Brawijaya University
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Evaluating Double Resampling through Simulation and Application in Semiparametric Truncated Spline for Waste Economic Value Kamelia Hidayat; Adji Achmad Rinaldo Fernandes; Atiek Iriany; Moh. Zhafran Hidayatulloh
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.26773

Abstract

This study developed a double resampling procedure as a method for estimating standard error in truncated spline semiparametric path modeling, given that standard error cannot be obtained analytically. Primary data were collected from 100 respondents through a Likert scale questionnaire and analyzed using a path structure involving Facility and Infrastructure Quality and Waste Bank Participation have a significantly positive effect on 3R-Based Waste Management Practices and the Waste Economic Value . The modeling process involved selecting knots, estimating spline functions, and evaluating double resampling performance through simulation studies. The results showed that and had a significant positive effect on and , while the relationship between and was negative before and after the 21% threshold. The simulation study shows that the Jackknife-Bootstrap method produces lower standard errors and bias, while the Bootstrap-Jackknife method is more stable at very small sample size. These findings confirm the effectiveness of double resampling.
Integrating Clustering and Hybrid Nonparametric Path Modeling for Waste Management Behavior in Batu City Moh Zhafran Hidayatulloh; Solimun Solimun; Adji Achmad Rinaldo Fernandes; Anggun Fadhila Rizqia; Fachira Haneinanda Junianto
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.26671

Abstract

This study formulates a hybrid nonparametric path analysis utilizing truncated spline-Fourier series integrated with Fuzzy C-Means clustering methodologies to investigate nonlinear behavioral patterns in community-based waste management. The model was utilized on survey data from 210 respondents in Bumiaji District, Batu City, encompassing Environmental Quality, Use of Waste Banks, Use of the 3R Principles, and Economic Benefits from Waste. Two distinct behavioral groups with varying emphasis on Use of Waste Banks and Environmental Quality were identified by the analysis. The hybrid model obtained a high coefficient of determination (0.891) and captures nonlinear relationships more successfully than the traditional linear approach. These results emphasize how crucial nonlinear behavioral dynamics are in influencing waste management behavior/decisions. The proposed framework helps local governments create more focused and efficient waste-management plans by offering a useful and adaptable analytical for understanding community behavior.
Nonparametric Path Modeling with Double Resampling for Waste Economic Value Utilization: Simulation-Based Performance Comparison Kamelia Hidayat; Adji Achmad Rinaldo Fernandes; Atiek Iriany; Solimun Solimun; Moh. Zhafran Hidayatulloh; Fachira Haneinanda Junianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.37218

Abstract

Waste generation exceeding landfill capacity highlights the urgency of realizing its economic value. This study analyzes the effect of Quality of Facilities and Infrastructure (X1) and Use of Waste Banks (X2) on Waste Management-Based 3R (Y1) and Waste Economic Value Utilization (Y2) using a truncated spline nonparametric path model. This study evaluates the performance of a nonparametric path analysis model based on truncated spline combined with a double resampling. Data were collected using a Likert scale questionnaire on community perceptions of waste’s economic benefits in Batu City. Simulation results show that the Jackknife-Bootstrap method achieves the lowest average bias (0.058), outperforming single resampling approaches such as Single-Bootstrap (0.178) and Single-Jackknife (0.176). Empirical findings indicate that improvements in the Quality of Facilities and Infrastructure  (X1) and Waste Bank Use (X2) significantly enhance Waste Management Based 3R (Y1) and Utilization of Waste Economic Value (Y2). The truncated spline model reveals a saturation effect, where the marginal benefits of X1 and X2 decrease beyond a threshold. Furthermore, Y1 positively affects Y2, emphasizing the importance of efficient waste management in enhancing economic value. The results support policies promoting balanced infrastructure development, community empowerment, and institutional innovation for sustainable circular economy implementation.
Modified Ramsey RESET in Combined Truncated Spline–Fourier Nonparametric Path Analysis on Waste Management Behavior Moh Zhafran Hidayatulloh; Solimun Solimun; Adji Achmad Rinaldo Fernandes; Anggun Fadhila Rizqia; Fachira Haneinanda Junianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.37239

Abstract

Nonparametric path analysis is a statistical approach that does not require the functional form of relationships between variables to be known a priori. Classical path analysis assumes linearity, which can be tested using the Ramsey Regression Specification Error Test (RESET). If the linearity test indicates that the relationships between variables are nonlinear, a nonparametric model can be applied. The purpose of this study is to develop a modified Ramsey RESET to identify nonparametric relationships modeled using truncated spline and Fourier series. The modified Ramsey RESET algorithm was successfully implemented to detect the optimal functional form of the nonparametric truncated spline and Fourier series and was subsequently applied to behavioral data on waste management practices. Furthermore, this study proposes an estimator for a hybrid nonparametric path model combining truncated spline and Fourier series approaches. The analysis results reveal that the best model integrates truncated spline with one and two knot points and a Fourier series with one oscillation. The model achieved an adjusted coefficient of determination of 0.956, indicating that it explains 95.6% of the variation in the Behavior of Transforming Waste into Economic Value, while the remaining 4.4% is explained by other unobserved factors outside the model.
Integrating Path Analysis and Kendall’s Tau-based Principal Component Analysis to Identify Determinants of Child Health Viky Iqbal Azizul Alim; Atiek Iriany; Adji Achmad Rinaldo Fernandes; Solimun Solimun; Candra Rezzining Wulat Sariro Weni Utomo
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.31156

Abstract

This study develops a latent variable path analysis model using a Mixed-Scale Principal Component Analysis (PCA) approach based on Kendall’s Tau correlation to identify key determinants of child health in Batu City, Indonesia. Primary data were collected from 100 mothers with children under five years old through questionnaires. The variables examined include Family Demographics, Nutritional Consumption, and Child Health Condition, each measured using mixed-scale indicators (ordinal and numerical). Kendall’s Tau-based PCA was applied to reduce data dimensionality and construct latent variables, which were then integrated into a path analysis model. The results show that maternal age is the most dominant indicator in shaping the Family Demographics construct, while balanced nutritional food is the strongest indicator forming the Nutritional Consumption construct. Path analysis further reveals that Family Demographics significantly affect Child Health Condition both directly and indirectly through Nutritional Consumption, with a coefficient of determination of 77.62\%. These findings underscore the critical role of demographic and nutritional factors in determining child health outcomes and highlight the methodological advantage of Kendall’s Tau-based mixed-scale PCA for analyzing heterogeneous indicator data within a structural path framework.
A Combined Truncated Spline and Kernel Semiparametric Path Model Development Usriatur Rohma; Adji Achmad Rinaldo Fernandes; Suci Astutik; Solimun Solimun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of 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.
Structural Equation Modeling Semiparametric Truncated Spline in Banking Credit Risk Behavior Models Devi Veda Amanda; Atiek Iriany; Adji Achmad Rinaldo Fernandes; Solimun Solimun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29769

Abstract

Housing is one of the primary needs for every individual. Along with the increasing population growth in Indonesia, the need for housing has also experienced a significant surge. This study aims to analyze the effect of customer attitudes on compliance behavior, fear of paying late, and timeliness of payment on Home Ownership Credit (KPR) customers at X Bank. Using a semiparametric Structural Equation Modeling (SEM) approach, this study examines the relationship between these variables to provide a deeper understanding of the factors that influence customer payment behavior. The data used in this study are primary data obtained through questionnaires distributed to 100 Bank X mortgage customers. The results of the analysis show that there is a significant influence between customer attitudes (X1) on obedient payment behavior (Y1) and fear of paying late (Y2), as well as timeliness of payment (Y3). The estimated coefficients obtained show a positive relationship between compliance behavior and timeliness of payment, and a negative relationship between fear of paying late and timeliness of payment, with a p-value 0.001 indicating statistical significance. This finding indicates that good customer attitudes can improve payment timeliness, while poor attitudes can lead to fear of paying late, which in turn can affect payment timeliness.
Co-Authors Anggun Fadhila Rizqia Atiek Iriany Candra Rezzining Wulat Sariro Weni Utomo Devi Veda Amanda Fachira Haneinanda Junianto Kamelia Hidayat Moh Zhafran Hidayatulloh Moh. Zhafran Hidayatulloh Solimun, Solimun Suci Astutik Usriatur Rohma Viky Iqbal Azizul Alim