The analysis of structural equation models by means of derivative free nonlinear least squares

Modeling using structural equations, is a second generation statistical data analysis technique, it has been positioned as the methodological options most used by researchers in various fields of science. The best known method is the covariance-based approach, but it presents some limitations for its application in certain cases. Another alternative method is based on the variance structure, through the analysis of partial least squares, which is an appropriate option when the research involves the use of latent variables (for example, composite indicators) prepared by the researcher, and where it is necessary to explain and predict complex models. This article presents a brief summary of the structural equation modeling technique, with an example on the relationship of constructs, sustainability and competitiveness in iron mining, and is intended to be a brief guide for future researchers in the engineering sciences. Keywords: Competitiveness, Structural equations, Iron mining, Sustainability. References [1]J. Hair, G. Hult, C. Ringle and M. Sarstedt. A Primer on Partial Least Square Structural Equation Modeling (PLS-SEM). California: United States. Sage, 2017. [2]H. Wold. Model Construction and Evaluation when Theoretical Knowledge Is Scarce: An Example of the Use of Partial Least Squares. Genève. Faculté des Sciences Économiques et Sociales, Université de Genève. 1979. [3]J. Henseler, G. Hubona & P. Ray. “Using PLS path modeling new technology research: updated guidelines”. Industrial Management & Data Systems, 116(1), 2-20. 2016. [4]G. Cepeda and Roldán J. “Aplicando en la Práctica la Técnica PLS en la Administración de Empresas”. Congreso de la ACEDE, Murcia, España, 2004. [5]D. Garson. Partial Least Squares. Regresión and Structural Equation Models. USA. Statistical Associates Publishing: 2016. [6]D. Barclay, C. Higgins & R. Thompson. “The Partial Least Squares (PLS) Approach to Causal Modeling: Personal Computer Adoption and Use as an Illustration”. Technology Studies. Special Issue on Research Methodology. (2:2), pp. 285-309. 1995. [7]J. Medina, N. Pedraza & M. Guerrero. “Modelado de Ecuaciones Estructurales. Un Enfoque de Partial Least Square Aplicado en las Ciencias Sociales y Administrativas”. XIV Congreso Internacional de la Academia de Ciencias Administrativas A.C. (ACACIA). EGADE – ITESM. Monterrey, México, 2010. [8]J. Medina & J. Chaparro. “The Impact of the Human Element in the Information Systems Quality for Decision Making and User Satisfaction”. Journal of Computer Information Systems. (48:2), pp. 44-52. 2008. [9]D. Leidner, S. Carlsson, J. Elam & M. Corrales. “Mexican and Swedish Managers’ Perceptions of the Impact of EIS on Organizational Intelligence, Decisión Making, and Structure”. Decision Science. (30:3), pp. 633-658. 1999.[10]W. Chin. “The partial least squares approach for structural equation modeling”. Chapter Ten, pp. 295-336 in Modern methods for business research. Edited by Macoulides, G. A., New Jersey: Lawrence Erlbaum Associates, 1998. [11]M. Höck & C. Ringle M. “Strategic networks in the software industry: An empirical analysis of the value continuum”. IFSAM VIIIth World Congress, Berlin 2006. [12]J. Henseler, Ch. Ringle & M. Sarstedt. Handbook of partial least squares: Concepts, methods and applications in marketing and related fields. Berlin: Springer, 2012. [13]S. Daskalakis & J. Mantas. “Evaluating the impact of a service-oriented framework for healthcare interoperability”. Studies in Health Technology and Informatics. pp. 285-290. 2008. [14]C. Fornell & D. Larcker: “Evaluating Structural Equation Models with Unobservable Variables and Measurement Error”, Journal of Marketing Research, vol. 18, pp. 39-50. Februay 1981. [15]C. Fornell. A Second Generation of Multivariate Analysis: An Overview. Vol. 1. New York, U.S.A. Praeger Publishers: 1982. [16]R. Falk and N. Miller. A Primer for Soft Modeling. Ohio: The University of Akron. 1992. [17]M. Martínez. Aplicación de la técnica PLS-SEM en la gestión del conocimiento: un enfoque técnico práctico. Revista Iberoamericana para Investigación y el Desarrollo Educativo. Vol. 8, Núm. 16. 2018. [18]S. Geisser. “A predictive approach to the random effects model”. Biometrika, Vol. 61(1), pp. 101-107. 1974. [19]J. Cohen. Statistical power analysis for the behavioral sciences. Mahwah, NJ: Lawrence Erlbaum, 1988. [20]GRI (2013). G4 Sustainability Reporting Guidelines. Global Reporting Initiative. Available: www.globalreporting.org

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Evaluation of Structural Equation Models Using the Partial Least Squares (PLS) Approach

Handbook of Partial Least Squares ◽

10.1007/978-3-540-32827-8_30 ◽

2009 ◽

pp. 691-711 ◽

Cited By ~ 244

Author(s):

Oliver Götz ◽

Kerstin Liehr-Gobbers ◽

Manfred Krafft

Keyword(s):

Least Squares ◽

Partial Least Squares ◽

Structural Equation ◽

Structural Equation Models

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Correcting measurement error bias in interaction models with small samples

Advances in Methodology and Statistics ◽

10.51936/wbtj1056 ◽

2006 ◽

Vol 3 (2) ◽

Author(s):

Josep Bisbe ◽

Germà Coenders ◽

Willem Saris ◽

Joan Batista-Foguet

Keyword(s):

Measurement Error ◽

Least Squares ◽

Structural Equation ◽

Structural Equation Models ◽

Ordinary Least Squares ◽

Alternative Methods ◽

Small Samples ◽

Least Squares Regression ◽

Interaction Terms ◽

Error Bias

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression.

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