Nonlinear Principal Component Analysis with Mixed Data Formative Indicator Models in Path Analysis

Authors

  • Rindu Hardianti Departement of Statistics, University of Brawijaya
  • Solimun Solimun Departement of Statistics, University of Brawijaya
  • Nurjannah Nurjannah Departement of Statistics, University of Brawijaya
  • Rosita Hamdan Department of Development Economics, University Malaysia Serawak, Malaysia

DOI:

https://doi.org/10.31764/jtam.v8i1.17559

Keywords:

Nonlinear Principal Component Analysis, Path Analysis, Mixed Data, Formative Indicator Models.

Abstract

This research aims to obtain the main component score of the latent variable ability to pay, determine the strongest indicators forming the ability to pay on a mixed scale based on predetermined indicators, and model the ability to pay on time as mediated by fear of paying using path analysis. The data used is secondary data obtained through distributing questionnaires with a mixed data scale. The sampling technique used in the research was purposive sampling. The number of samples used in the research was 100 customers. The method used is nonlinear principal component analysis with path analysis modeling. The results of this research show that of the five indicators formed by the Principal Component, 74.8% of diversity or information is able to be stored, while 25.20% of diversity or other information is not stored (wasted). Credit term is the strongest indicator that forms the ability to pay variable. The variable ability to pay mortgage has a significant effect on payments by mediating the fear of being late in paying with a coefficient of determination of 73.63%.

 

Author Biographies

Rindu Hardianti, Departement of Statistics, University of Brawijaya

Rindu Hardianti, born November 24th 2000 in Denpasar. Bachelor degree in Statistics obtained from Department of Statistics, Faculty of Mathematics and Science Natural Sciences, Brawijaya University. In 2023. Currently underway Master's Degree in Statistics Department, Faculty Mathematics and Natural Sciences, University Brawijaya.

Solimun Solimun, Departement of Statistics, University of Brawijaya

Solimun, born December 15th 1961 in Malang, since 1987 until now he has worked as a lecturer Brawijaya University, Malang. Get a Bachelor's degree Agriculture obtained from the Department of Agronomy, Faculty Agriculture, Brawijaya University (1986). Title Master of Science in Statistics obtained from Department of Statistics, Bogor Agricultural Institute (1993). Doctorate Degree in Mathematics and Science Nature obtained from FMIPA, Airlangga University Surabaya (1997). This book is a written work the 10th is about research methodology and Data analysis method.

Nurjannah Nurjannah, Departement of Statistics, University of Brawijaya

Nurjannah, born September 21th 1980 in Malang, since 2005 until now working as Lecturer at Brawijaya University, Malang. Get a Bachelor's degree Statistics obtained from the Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University (2003). Master's Degree Philosophy in the field of Financial Econometrics obtained from the Faculty of Business and Economics, Monash University, Australia (2009). Doctorate degree Philosophy in the field of Financial Econometrics obtained from the Faculty of Business and Economics, Monash University. Courses taught by authors include: Microeconomics, Econometrics, Stochastic Processes, Statistical Methods and Introduction Probability Theory. A book that was once a masterpiece authors include: Multivariate Statistical Methods: Structural Equation Modeling (SEM), WarpPLS Approach and Statistical Methods Multivariate: Generalized Structured Component Analysis (GSCA).

References

Astutik, S., Solimun, & Darmanto. (2018). Multivariate Analysis: Theory and Application with SAS. Brawijaya Press University. https://books.google.co.id/books/about/Analisis_Multivariat.html?id=BvhqDwAAQBAJ&redir_esc=y

Budiono, D. (2016). The behavior of corporate taxpayers in fulfilling tax obligations: Humanistic theory perspective. FEBSOS. http://jonuns.com/index.php/journal/article/view/542

Cahyoningtyas, R. A., Solimun, & Fernandes, A. A. R. (2020). The implementation of first order and second order with mixed measurement to identify farmers satisfaction. Mathematics and Statistics, 8(6), 671–682. https://doi.org/https://doi.org/10.13189/ms.2020.080607

Chen, B., Yang, J., Jeon, B., & Zhang, X. (2017). Kernel quaternion principal component analysis and its application in RGB-D object recognition. Neurocomputing, 266, 293–303. https://doi.org/https://doi.org/10.1016/j.neucom.2017.05.047

David, C. C., & Jacobs, D. J. (2014). Principal component analysis: a method for determining the essential dynamics of proteins. Protein Dynamics: Methods and Protocols, 1084, 193–226. https://doi.org/https://doi.org/10.1007/978-1-62703-658-0_11

Demir, C., & Keskin, S. (2022). Introduction of Nonlinear Principal Component Analysis with an Application in Health Science Data. Eastern Journal of Medicine, 27(3), 394–402. https://doi.org/10.5505/ejm.2022.09068

Efendi, E. C. L., Fernandes, A. A. R., & Mitakda, M. B. T. (2021). Modeling of Path Nonparametric Truncated Spline Linear, Quadratic, and Cubic in Model on Time Paying Bank Credit. WSEAS Transactions on International Journal of Electrical Engineering and Computer Science, 3, 52–60. https://doi.org/https://doi.org/10.13189/ms.2021.090611

Fernandes, A. A. R., & Solimun. (2017). Moderating effects orientation and innovation strategy on the effect of uncertainty on the performance of business environment. International Journal of Law and Management, 59(6), 1211–1219. https://doi.org/10.1108/IJLMA-10-2016-0088

Gewers, F., Ferreira, G. R., Arruda, H. F. de, & Silva, F. N. (2021). Principal Component Analysis: A Natural Approach to Data Exploration. ACM Computing Surveys (CSUR), 54(4), 1–34. https://doi.org/https://doi.org/10.1145/3447755

Heo, S., & Lee, J. H. (2019). Parallel neural networks for improved nonlinear principal component analysis. Computers & Chemical Engineering, 127, 1–10. https://doi.org/https://doi.org/10.1016/j.compchemeng.2019.05.011

Jiang, Q., & Yan, X. (2015). Nonlinear plant-wide process monitoring using MI-spectral clustering and Bayesian inference-based multiblock KPCA. Journal of Process Control, 32, 38–50. https://doi.org/https://doi.org/10.1016/j.jprocont.2015.04.014

Jolliffe, I. T., & Cadima, J. (2016). Principal Component Analysis: A Review and Recent Developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065), 20150202. https://doi.org/https://doi.org/10.1098/rsta.2015.0202

Katayama, H., Mori, Y., & Kuroda, M. (2022). Variable Selection in Nonlinear Principal Component Analysis. In Advances in Principal Component Analysis (pp. 79–89). IntechOpen. https://doi.org/http://dx.doi.org/10.5772/intechopen.103758

Kock, N. (2016). Advantages of nonlinear over segmentation analyses in path models. International Journal of E-Collaboration (Ijec), 12(4), 1–6. https://doi.org/https://doi.org/10.4018/ijec.2016100101

Mori, Y., Kuroda, M., & Makino, N. (2016). Nonlinear Principal Component Analysis and Its Applications. Springer Singapore. https://doi.org/https://doi.org/10.1007/978-981-10-0159-8

Solimun, S; Fernandes, A. A. R. & N. (2017). Metode Statistika Multivariat. Pemodelan Persamaan Struktural (SEM). UB Press. https://books.google.co.id/books?hl=id&lr=&id=GrRVDwAAQBAJ&oi=fnd&pg=PR5&dq=Solimun,+S%3B+Fernandes,+A.+A.+R.+%26+N.+(2017).+Metode+Statistika+Multivariat.+Pemodelan+Persamaan+Struktural+(SEM).+UB+Press.&ots=nva-f-b8cH&sig=f-mwQtLFiSsdF1YW4NNdyqGj-fw&redir_esc=y#v=onepage&q&f=false

Solimun, & Fernandes, A. A. R. (2017). Investigation of the mediating variable: What is necessary? (case study in management research). 59(6), 1059–1067. https://doi.org/https://doi.org/10.1108/IJLMA-09-20 16 -0077

Sumardi, S., & Fernandes, A. A. R. (2018). The mediating effect of service quality and organizational commitment on the effect of management process alignment on higher education performance in Makassar, Indonesia. Journal of Organizational Change Management, 31(2), 410–425. https://doi.org/https://doi.org/10.1108/JOCM-11-2016-0247

Vegelius, J., & Jin, S. (2021). A semiparametric approach for structural equation modeling with ordinal data. Structural Equation Modeling. A Multidisciplinary Journal, 28(4), 497–505. https://doi.org/https://doi.org/10.1080/10705511.2020.1848431

Yu, H., Khan, F., & Ikram, G. (2015). An alternative formulation of PCA for process monitoring using distance correlation. Industrial & Engineering Chemistry Research, 55(3), 656–669. https://doi.org/https://doi.org/10.1021/acs.iecr.5b03397

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Published

2024-01-19

Issue

Vol. 8 No. 1 (2024): January

Section

Articles

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