Multivariate Adaptive Regression Spline Partial Least Square Dengan Elastic NET

Dukalang, Hendra H (2026) Multivariate Adaptive Regression Spline Partial Least Square Dengan Elastic NET. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pemodelan variabel laten dalam Structural Equation Modeling Partial Least Square pada umumnya dibangun dengan asumsi hubungan linier antar variabel laten, dengan estimasi skor variabel laten dilakukan menggunakan algoritma PLS. Akan tetapi ketika hubungan antara variabel laten tersebut nonlinier dan bentuk fungsionalnya tidak diketahui secara eksplisit, pendekatan linier kurang memadai sehingga diperlukan pengembangan model SEM nonlinier. Salah satu pendekatan yang digunakan adalah Multivariate Adaptive Regression Spline Partial Least Square (MARSPLS) juga menangkap pola nonlinier dan interksi melalui fungsi basis adaptif dan cenderung menghasilkan model dengan kompleksitas tinggi akibat pembentukan basis fungsi serata berpotensi menimbulkan masalah multikolinieritas. Oleh karena itu, penelitian ini tidak hanya mengembangkan model SEM nonlinier, tetapi juga mengusulkan regularisasi parameter untuk menghasilkan model yang lebih parsimonious dan stabil melalui pengembangan model Multivariate Adaptive Regression Spline Partial Least Square dengan Elastic Net (MARSPLS-EN). Pendekatan Elastic Net untuk seleksi variabel sekaligus mengatasi permasalahan multikolinieritas melalui kombinasi penalti dan . Hasil kajian metodologis menunjukkan bahwa estimasi parameter pada model MARSPLS dengan metode Ordinary Least Square menunjukkan hasil yang closed-form. Model MARSPLS-EN dengan metode Penalized Least Square menghasilkan penaksir yang tidak closed form sehingga di selesaikan dengan pendekatan Coordinat Descent Algorithm. Studi simulasi menunjukkan bahwa estimator pada Model MARSPLS-EN tanpa interaksi, 2 interaksi dan 3 interaksi bersifat konsisten yang ditunjukkan oleh semakin besar jumlah sampel dan varians eror semakin kecil maka nilai RMSE juga semakin kecil. Kedua model diaplikasikan pada data empiris pemodelan M-UTAUT untuk menganalisis niat berperilaku pengguna E-Wallet di Indonesia. Hasil empiris menunjukkan bahwa model MARSPLS menghasilkan kinerja terbaik dibandingkan dengan SEMPLS dan MARSPLS-EN berdasarkan nilai dari BIC. sedangkan MARSPLS-EN mampu mereduksi kompleksitas model dan jumlah fungsi basis secara signifikan.
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Modeling latent variables in Partial Least Squares Structural Equation Modeling (PLS-SEM) is generally based on the assumption of linear relationships among latent variables, with latent variable scores estimated using the PLS algorithm. However, when the relationships among these latent variables are nonlinear and their functional forms are not explicitly known, a linear approach is insufficient, necessitating the development of nonlinear SEM models. One approach used is Multivariate Adaptive Regression Spline Partial Least Squares (MARSPLS), which also captures nonlinear patterns and interactions through adaptive basis functions but tends to produce highly complex models due to the formation of basis functions and has the potential to cause multicollinearity issues. Therefore, this study not only develops a nonlinear SEM model but also proposes parameter regularization to produce a more parsimonious and stable model through the development of the Multivariate Adaptive Regression Spline Partial Least Squares with Elastic Net (MARSPLS-EN) model. The Elastic Net approach is used for variable selection while simultaneously addressing the issue of multicollinearity through a combination of the L1 and L2 penalties. The results of the methodological analysis show that parameter estimates in the MARSPLS model using the Ordinary Least Squares method yield closed-form results. The MARSPLS-EN model using the Penalized Least Squares method produces non-closed-form estimators, which are therefore solved using the Coordinate Descent Algorithm. Simulation studies show that the estimators in the MARSPLS-EN model – with no interactions, two interactions, and three interactions are consistent, as evidenced by the fact that as the sample size increases and the error variance decreases, the RMSE value also decreases. Both models were applied to empirical data from the M-UTAUT model to analyze the behavioral intentions of e-wallet users in Indonesia. The empirical results show that the MARSPLS model performs best compared to SEMPLS and MARSPLS-EN based on BIC values, while MARSPLS-EN is able to significantly reduce model complexity and the number of basis functions.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	SEM nonlinier, PLS, MARSPLS, Elastic Net, MARSPLS-EN, Regularisasi Parameter Nonlinear SEM, PLS, MARSPLS, Elastic Net, MARSPLS-EN, Parameter Regularization.
Subjects:	H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics Q Science > QA Mathematics > QA278.3 Structural equation modeling.
Divisions:	Faculty of Mathematics and Science > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Hendra H. Dukalang
Date Deposited:	05 Aug 2026 04:19
Last Modified:	05 Aug 2026 05:43
URI:	http://repository.its.ac.id/id/eprint/143997

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