Volume 7, Issue 1 (January 2020), Pages: 108-116

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 Original Research Paper

 Title: Use of nonparametric regression in mode B type measurement model: A simulation study approach

 Author(s): Syed Jawad Ali Shah *, Qamruz Zaman

 Affiliation(s):

 Department of Statistics, University of Peshawar, Peshawar, Pakistan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-0579-1935

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.01.011

 Abstract:

In the conventional PLS-path modeling, the relationship among latent variables (LVs) is estimated by fitting a simple/multiple linear regression lines. For this purpose, researchers have to assume that the endogenous LV is the linear function of exogenous LVs, which is rarely met in real data analysis. The statisticians have devised a non-linear model-fitting approach to overcome the issue of linearity, but for that purpose, one should assume some specific functional form like quadratic, cubic or some degree of a polynomial in advance. Hence, when the linearity assumption is violated, the only appropriate choice is to use the nonparametric regression approaches. This study is mainly focused on the estimation of the latent variable model by incorporating three nonparametric smoothing procedures: Kernel regression estimate, local polynomial estimate, and smoothing spline estimates. An algorithm for LV models is proposed and presented based on nonparametric regression approaches for the mode B type measurement model (i.e., formative model). From simulation studies, it was clearly concluded that nonparametric based LV modeling approaches perform well for large sample sizes (i.e., for sample size 100 and above) as compared to standard PLS-path modeling procedure. However, for small samples (less than 100 observations), the standard PLS-path modeling procedure was giving better results. 

 © 2019 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Latent variable model, Nonparametric regression, PLS-Path model, Formative model

 Article History: Received 18 August 2019, Received in revised form 11 November 2019, Accepted 12 November 2019

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Shah SJA and Zaman Q (2020). Use of nonparametric regression in mode B type measurement model: A simulation study approach. International Journal of Advanced and Applied Sciences, 7(1): 108-116

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 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6

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 References (15) 

1. Fan J and Gijbels I (1996). Local polynomial modelling and its applications. Chapman and Hall, London, UK.   [Google Scholar]
2. Györfi L, Kohler M, Krzyzak A, and Walk H (2002). A distribution-free theory of nonparametric regression. Springer Science and Business Media, New York, USA. https://doi.org/10.1007/b97848   [Google Scholar]
3. Härdle W (1990). Applied nonparametric regression (No. 19). Cambridge University Press, Cambridge, USA. https://doi.org/10.1017/CCOL0521382483   [Google Scholar]
4. Härdle WK, Müller M, Sperlich S, and Werwatz A (2004). Nonparametric and semiparametric models: An introduction. Springer, New York, USA. https://doi.org/10.1007/978-3-642-17146-8   [Google Scholar]
5. Kelava A, Kohler M, Krzyżak A, and Schaffland TF (2017). Nonparametric estimation of a latent variable model. Journal of Multivariate Analysis, 154: 112-134. https://doi.org/10.1016/j.jmva.2016.10.006   [Google Scholar]
6. Lohmöller JB (1989). Latent variable path modeling with partial least squares. Springer-Verlag Berlin Heidelberg, Berlin, Germany. https://doi.org/10.1007/978-3-642-52512-4   [Google Scholar]
7. Monecke A and Leisch F (2012). SEMPLS: Structural equation modeling using partial least squares. Journal of Statistical Software, 48(3): 1-32. https://doi.org/10.18637/jss.v048.i03   [Google Scholar]
8. Paxton P, Curran PJ, Bollen KA, Kirby J, and Chen F (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8(2): 287-312. https://doi.org/10.1207/S15328007SEM0802_7   [Google Scholar]
9. Sanchez G and Trinchera L (2012). PLS-PM: Partial least squares data analysis methods. Available online at: https://bit.ly/36rb1ko
10. Sanchez G, Trinchera L, and Russolillo G (2015). PLS-PM: An R package for partial least squares path modeling. Available online at: https://bit.ly/36G5Jlx
11. Sen PK (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, 63(324): 1379-1389. https://doi.org/10.1080/01621459.1968.10480934   [Google Scholar]
12. Wand MP and Jones MC (1995). Kernel smoothing. Chapman and Hall, London, UK. https://doi.org/10.1007/978-1-4899-4493-1   [Google Scholar]
13. Wold H (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiaah PR (Ed.), Multivariate analysis: 391-420. Academic Press, New York, USA.   [Google Scholar]
14. Wold H (1973). Nonlinear iterative partial least squares (NIPALS) modeling: Some current. In: Krishnaiah PR (Ed.), Multivariate analysis: In the international symposium on multivariate analysis: 383-407. Academic Press, New York, USA. https://doi.org/10.1016/B978-0-12-426653-7.50032-6   [Google Scholar]
15. Wold H (1982). Soft modeling: the basic design and some extensions. In: Jőreskog KG and Wold H (Ed.), Systems under indirect observations: Causality, structure, prediction-part 2: 1-54. North-Holland Publisher, Amsterdam, Netherlands.   [Google Scholar]