Non-Normality Propagation among Latent Variables and Indicators in PLS-SEM Simulations

Structural equation modeling employing the partial least squares method (PLS-SEM) has been extensively used in business research. Often the use of this method is justified based on claims about its unique performance with small samples and non-normal data, which call for performance analyses. How normal and non-normal data are created for the performance analyses are examined. A method is proposed for the generation of data for exogenous latent variables and errors directly, from which data for endogenous latent variables and indicators are subsequently obtained based on model parameters. The emphasis is on the issue of non-normality propagation among latent variables and indicators, showing that this propagation can be severely impaired if certain steps are not taken. A key step is inducing non-normality in structural and indicator errors, in addition to exogenous latent variables. Illustrations of the method and its steps are provided through simulations based on a simple model of the effect of e-collaboration technology use on job performance.

[1]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo Evidence , 1981 .

[2]  Ned Kock,et al.  Advanced Mediating Effects Tests, Multi-Group Analyses, and Measurement Model Assessments in PLS-Based SEM , 2014, Int. J. e Collab..

[3]  C. Haas,et al.  Estimation of averages in truncated samples , 1990 .

[4]  Robert C. MacCallum,et al.  Representing sources of error in the common-factor model: Implications for theory and practice. , 1991 .

[5]  Erik Hjalmarsson,et al.  Jackknifing Stock Return Predictions , 2008 .

[6]  Hoon Kim,et al.  Monte Carlo Statistical Methods , 2000, Technometrics.

[7]  P. Hackl,et al.  Robustness of partial least-squares method for estimating latent variable quality structures , 1999 .

[8]  Léopold Simar,et al.  Computer Intensive Methods in Statistics , 1994 .

[9]  Jan-Bernd Lohmöller,et al.  Latent Variable Path Modeling with Partial Least Squares , 1989 .

[10]  N. Kock,et al.  The impact of individualism on buyer–supplier relationship norms, trust and market performance: An analysis of data from Brazil and the U.S.A. , 2012 .

[11]  Todd C. Headrick.  Statistical Simulation: Power Method Polynomials and Other Transformations , 2009 .

[12]  Marko Sarstedt,et al.  PLS-SEM: Indeed a Silver Bullet , 2011 .

[13]  Allen I. Fleishman.  A method for simulating non-normal distributions , 1978 .

[14]  Yang-Heui Ahn,et al.  Quality of nursing doctoral education in Korea: towards policy development. , 2012, Journal of advanced nursing.

[15]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[16]  J. Gastwirth,et al.  A robust modification of the Jarque–Bera test of normality , 2008 .

[17]  M. A. Cirillo,et al.  Robust Regression Estimates in the Prediction of Latent Variables in Structural Equation Models , 2012 .

[18]  S. Wold,et al.  Some recent developments in PLS modeling , 2001 .

[19]  Luc Cassivi,et al.  The Impact of E‐collaboration Tools on Firms' Performance , 2004 .

[20]  A. M. Ulvnes,et al.  If the Supplier's Human Capital Walks Away, Where Would the Customer Go? , 2011 .

[21]  S. Mattson,et al.  How to Generate Non-normal Data for Simulation of Structural Equation Models. , 1997, Multivariate behavioral research.

[22]  Robert Tibshirani,et al.  Resampling Methods of Estimation , 2001 .

[23]  Yawen Chen,et al.  Process quality and collaboration quality on B2B e-commerce , 2013, Ind. Manag. Data Syst..

[24]  Ned Kock,et al.  Lateral Collinearity and Misleading Results in Variance-Based SEM: An Illustration and Recommendations , 2012, J. Assoc. Inf. Syst..

[25]  Catherine E. Connelly,et al.  Understanding Nonmalicious Security Violations in the Workplace: A Composite Behavior Model , 2011, J. Manag. Inf. Syst..

[26]  Todd C. Headrick.  Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions , 2002 .

[27]  P. Lytsy,et al.  Adherence to and beliefs in lipid-lowering medical treatments: a structural equation modeling approach including the necessity-concern framework. , 2013, Patient education and counseling.

[28]  Peter J. Knez,et al.  On The Robustness of Size and Book‐to‐Market in Cross‐Sectional Regressions , 1997 .

[29]  Ned Kock,et al.  Using WarpPLS in E-collaboration Studies: An Overview of Five Main Analysis Steps , 2010, Int. J. e Collab..

[30]  S. Wilson,et al.  Market access, population density, and socioeconomic development explain diversity and functional group biomass of coral reef fish assemblages , 2012 .