A hybrid method combining the PLS and the Bayesian approaches to estimate the Structural Equation Models


Abstract


The purpose of this paper is to provide a hybrid method combining the Partial Least Squares and the Bayesian approaches to estimate the Structural Equation Models. The aim advantage of this new method is to overcome the assumption of normality that is required in Bayesian approach. The results obtained from an application on simulated  and on real data show that our proposed method outperforms both PLS and Bayesian approaches in terms of standard errors.

DOI Code: 10.1285/i20705948v11n2p577

Keywords: Structural Equation Models, Partial Least Squares approach, Bayesian approach, Hybrid method.

References


Ansari, A., Jedidi, K., and Jagpal, S. (2000). A hierarchical bayesian methodology for treating heterogeneity in structural equation models. Marketing Science, 19(4):328– 347.

Chin, W. W. (1998). The partial least squares approach to structural equation modeling. Modern methods for business research, 295(2):295–336.

Ciavolino, E. and Al-Nasser, A. D. (2009). Comparing generalised maximum entropy and partial least squares methods for structural equation models. Journal of nonparametric statistics, 21(8):1017–1036.

Ciavolino, E. and Carpita, M. (2015). The gme estimator for the regression model with a composite indicator as explanatory variable. Quality & Quantity, 49(3):955–965.

Ciavolino, E., Carpita, M., and Al-Nasser, A. (2015). Modelling the quality of work in the italian social co-operatives combining npca-rsm and sem-gme approaches. Journal of Applied Statistics, 42(1):161–179.

Ciavolino, E. and Dahlgaard, J. J. (2009). Simultaneous equation model based on the generalized maximum entropy for studying the effect of management factors on enter- prise performance. Journal of applied statistics, 36(7):801–815.

Ciavolino, E. and Nitti, M. (2013). Simulation study for pls path modelling with high- order construct: A job satisfaction model evidence. In Advanced Dynamic Modeling of Economic and Social Systems, pages 185–207. Springer.

Dunson, D. B. (2000). Bayesian latent variable models for clustered mixed outcomes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(2):355– 366.

Fornell, C. and Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of marketing research, pages 39–50.

Hair, J. F., Sarstedt, M., Pieper, T. M., and Ringle, C. M. (2012). The use of partial least squares structural equation modeling in strategic management research: a review of past practices and recommendations for future applications. Long range planning, 45(5-6):320–340.

Hoyle, R. H. (2012). Handbook of structural equation modeling. Guilford Press.

Jedidi, K. and Ansari, A. (2001). Bayesian structural equation models for multilevel data. New developments and techniques in structural equation modeling, pages 129– 157.

J ̈oreskog, K. G. (1970). A general method for analysis of covariance structures. Biometrika, 57(2):239–251.

J ̈oreskog, K. G. and Wold, H. (1982). The ML and PLS techniques for modeling with latent variables: historical and comparative aspects. In J ̈oreskog, K. G. and Wold, H., editors, Systems Under Indirect Observation, Part 1, pages 263–270, North-Holland, Amsterdam.

Lee, S.-Y. (2007). Structural equation modeling: A Bayesian approach, volume 711. John Wiley & Sons.

Lee, S.-Y. and Song, X.-Y. (2003). Model comparison of nonlinear structural equation models with fixed covariates. Psychometrika, 68(1):27–47.

Lee, S.-Y. and Song, X.-Y. (2004). Evaluation of the bayesian and maximum likelihood approaches in analyzing structural equation models with small sample sizes. Multi- variate Behavioral Research, 39(4):653–686.

Lunn, D. J., Thomas, A., Best, N., and Spiegelhalter, D. (2000). Winbugs-a bayesian modelling framework: concepts, structure, and extensibility. Statistics and computing, 10(4):325–337.

Nitzl, C. (2016). The use of partial least squares structural equation modelling (pls- sem) in management accounting research: Directions for future theory development. Journal of Accounting Literature, 37:19–35.

Papalia, R. B. and Ciavolino, E. (2011). Gme estimation of spatial structural equations models. Journal of classification, 28(1):126–141.

Reinartz, W., Haenlein, M., and Henseler, J. (2009). An empirical comparison of the efficacy of covariance-based and variance-based sem. International Journal of research in Marketing, 26(4):332–344.

Sarstedt, M., Ringle, C. M., Smith, D., Reams, R., and Hair, J. F. (2014). Partial least squares structural equation modeling (pls-sem): A useful tool for family business researchers. Journal of Family Business Strategy, 5(1):105–115.

Song, X.-Y. and Lee, S.-Y. (2012). A tutorial on the bayesian approach for analyzing structural equation models. Journal of Mathematical Psychology, 56(3):135–148.

Tenenhaus, M., Amato, S., and Esposito Vinzi, V. (2004). A global goodness-of-fit index for pls structural equation modelling. In Proceedings of the XLII SIS scientific meeting, volume 1, pages 739–742.

Tenenhaus, M., Vinzi, V. E., Chatelin, Y.-M., and Lauro, C. (2005). Pls path modeling. Computational statistics & data analysis, 48(1):159–205.

Vinzi, V. E., Trinchera, L., and Amato, S. (2010). Pls path modeling: from foundations to recent developments and open issues for model assessment and improvement. In Handbook of partial least squares, pages 47–82. Springer.

Wetzels, M., Odekerken-Schr ̈oder, G., and Van Oppen, C. (2009). Using pls path model- ing for assessing hierarchical construct models: Guidelines and empirical illustration. MIS quarterly, pages 177–195.

Wold, H. (1982). Soft modelling: the basic design and some extensions. Systems under indirect observation, Part II, pages 36–37.

Wold, H. (1985). Partial least squares. Encyclopedia of statistical sciences.

Yang, M. and Dunson, D. B. (2010). Bayesian semiparametric structural equation models with latent variables. Psychometrika, 75(4):675–693.

Yanuar, F. (2014). The estimation process in bayesian structural equation modeling approach. In Journal of Physics: Conference Series, volume 495, page 012047. IOP Publishing.

Zarrouk, Z. (2008). Injustice, compensation et qualit ́e de la relation: le cas d’une d ́efaillance volontaire - le surbooking. PhD thesis, Pau.


Full Text: pdf


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.