Spearman Rank Correlation PCA for Mixed Scale Indicator in Structural Equation Modeling

Lisa Asaliontin, Eni Sumarminingsih, Solimun Solimun, Mohammad Ohid Ullah

Abstract


Structural Equation Modeling (SEM) is a statistical modeling technique that integrates measurement models and structural models simultaneously. In the SEM measurement model, not all latent variables are metric, they can be mixed scales, namely metric and non-metric which have not been widely studied. This study aims to apply the Spearman Rank Correlation Principal Component Analysis (PCA) to handle mixed-scale indicator data in a mixed measurement model (formative and reflective). This method is evaluated on a case study of fertilizer repurchase decisions, resulting in a total determination coefficient of 80%. This shows the flexibility of SEM in handling the complexity of mixed-scale data without sacrificing estimation accuracy. The results showed that the Spearman Rank Correlation PCA was able to store 78.62% of the diversity of data from mixed-scale indicator variables, namely Farmer Demographics (X2). In addition, the results showed that Customer Satisfaction (X1) significantly influenced Repurchase Decisions (Y2) but did not directly affect Customer Engagement (Y1). Farmer Demographics (X2) significantly influences Customer Engagement (Y1) and Repurchase Decisions (Y2), and Customer Engagement has a significant effect on Repurchase Decisions (Y2).


Keywords


Farmer Demographics; Fertilizer Repurchase Decision; Spearman Rank Correlation PCA; Structural Equation Modeling

Full Text:

PDF

References


[1] Solimun, Fernandes A. A. R., Nurjannah, “Metode Statistika Multivariat Pemodelan Persamaan Struktural (SEM)", UB Press, 2017. https://opac.perpusnas.go.id/DetailOpac.aspx?id=1141341

[2] Hair J.F., Black W. C., Babin B. J., and Anderson R. E., "Multivariate Data Analysis (Eighth Edition)", vol. 19, no. 3, 2019. DOI: 10.5117/2006.019.003.007.

[3] Ryu E., “Model fit evaluation in multilevel structural equation models,” Front. Psychol., vol. 5, no. FEB, pp. 1–9, 2014. DOI: 10.3389/fpsyg.2014.00081.

[4] Albahri A. S., Alnoor, A., Zaidan, A. A., Albahri, O. S., Hameed, H., Zaidan, B. B., Peh, S. S., Zain, A. B., Siraj, S. B., Alamoodi, A. H., & Yass, A. A.., “Based on the multi-assessment model: Towards a new context of combining the artificial neural network and structural equation modelling: A review,” Chaos, Solitons and Fractals, vol. 153, p. 111445, 2021. DOI: 10.1016/j.chaos.2021.111445.

[5] Chen H., and Wang Y., “A Penalized Spline Approach to Functional Mixed Effects Model Analysis,” Biometrics, vol. 67, no. 3, pp. 861–870, 2011. DOI: 10.1111/j.1541-0420.2010.01524.x.

[6] Watanabe K., Naito K., and Koch I., “Robustness of Principal Component Analysis with Spearman’s Rank Matrix,” J. Stat. Theory Pract., vol. 18, no. 1, pp. 1–29, 2024. DOI: 10.1007/s42519-023-00358-z.

[7] Solimun, Fernandes A. A. R., Nurjannah, Erwinda E. G., Hardianti R., and Arini L. H. Y., "Metodologi Penelitian Variabel Mining berbasis Big Data dalam Pemodelan Sistem untuk mengungkap Research Novelty", UB Press, 2023. https://books.google.co.id/books/about/Metodologi_Penelitian.html?id=GfXaEAAAQBAJ&redir_esc=y

[8] Yu H., Khan F., and Garaniya V., “A Sparse PCA for Nonlinear Fault Diagnosis and Robust Feature Discovery of Industrial Processes,” AIChE J., vol. 62, no. 5, pp. 215–228, 2016. DOI: 10.1002/aic.

[9] Ganguli S., and Roy S. K., “Generic technology-based service quality dimensions in banking: Impact on customer satisfaction and loyalty,” Int. J. Bank Mark., vol. 29, no. 2, pp. 168–189, 2011. DOI: 10.1108/02652321111107648.

[10] Bansal R., and Chaudhary K., “Customer Engagement- A Literature Review,” Glob. Int. Res. Thoughts, vol. 2, no. 1, pp. 15–20, 2016. [Online]. Available: https://www.researchgate.net/publication/318224473

[11] Karamizadeh S., Abdullah S. M., Manaf A. A., Zamani M., and Hooman A., “An Overview of Principal Component Analysis,” J. Signal Inf. Process., vol. 04, no. 03, pp. 173–175, 2013. DOI: 10.4236/jsip.2013.43b031.

[12] Jollife I. T., and Cadima J., “Principal component analysis: A review and recent developments,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 374, no. 2065, 2016. DOI: 10.1098/rsta.2015.0202.

[13] Kong X., Hu C., and Duan Z., "Principal component analysis networks and algorithms", 2017. DOI: 10.1007/978-981-10-2915-8.

[14] Roos J. M., and Bauldry S., "Confirmatory Factor Analysis. United States of America", SAGE Publications, 2022. https://books.google.co.id/books/about/Confirmatory_Factor_Analysis.html?id=sT1KEAAAQBAJ&redir_esc=y

[15] Goretzko D., Siemund K., and Sterner P., “Evaluating Model Fit of Measurement Models in Confirmatory Factor Analysis,” Educ. Psychol. Meas., vol. 84, no. 1, pp. 123–144, 2024. DOI: 10.1177/00131644231163813.

[16] Schreiber-Gregory D., and Bader K., “Logistic and Linear Regression Assumptions: Violation Recognition and Control,” SESUG Pap. 247, no. May, pp. 1–22, 2018, [Online]. Available: https://www.researchgate.net/publication/341354759

[17] Fernandes A. A. R., Solimun, Nurjannah, and Amaliana L., "Analisis Regresi Dalam Pendekatan Fleksibel (Ilustrasi dengan Paket Program R)", 2021. https://books.google.co.id/books/about/Analisis_Regresi_dalam_Pendekatan_Fleksi.html?id=SKFgEAAAQBAJ&redir_esc=y




DOI: https://doi.org/10.18860/cauchy.v10i1.29976

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Lisa Asaliontin, Eni Sumarminingsih, Solimun Solimun, Mohammad Ohid Ullah

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.