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

Abstract

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.

Minimum sample size estimation in PLS‐SEM: The inverse square root and gamma‐exponential methods

“…Using the Monte Carlo simulation (Kock, ; Paxton et al, ; Robert & Casella, ) method for minimum sample size estimation in PLS‐SEM requires the researcher to set a number of sample size points (e.g. 15, 20, 30 and 40), generate a number of samples (e.g.…”

“…Statistical power (Cohen, ; ; Goodhue et al, ; Kock, ; Muthén & Muthén, ), often referred to simply as ‘power’, is a statistical test's probability of avoiding type II errors, or false negatives. Power is often estimated for a particular coefficient of association and sample size, for samples drawn from a population, at a given significance level (usually P < .05).…”

“…We believe that they are valuable time‐saving tools to be used in the early cyclical phases of research design, and that can be significantly more precise than comparable early‐stage research heuristics currently used by researchers. More specifically, they are first‐step methods that researchers can use to address issues related to statistical power and minimum sample size requirements (Cohen, ; ; Goodhue et al, ; Kock, ).…”

Single missing data imputation in PLS-based structural equation modeling

“…The latent variables, which refer to theoretical constructs, are: communication flow orientation (C1), usefulness in the development of information technology (IT) solutions (C2), ease of understanding (C3), accuracy (C4), and impact on redesign success (C5). The mathematical symbols used in the model, and in the following sections, were adapted from the classic path analysis, covariance-based SEM, and PLS literatures (Kline, 2010;Kock, 2016;Lohmöller, 1989;Wright, 1934;1960): βij is the path coefficient for the link going from composite Cj to composite Ci, λij is the loading for the j th indicator of composite Ci, and ζi is the structural error associated with an endogenous composite Ci. With exception of communication flow orientation (C1), a set of indicators xij is used to measure each composite Ci.…”

“…The method of partial least squares (PLS) experienced explosive growth in the context of structural equation modeling (SEM), whereby latent variables are measured via indicators in questionnaires (Akter et al, 2017;Kock, 2016;Rigdon, 2016). Indicators frequently take the form of scores generated based on questionstatements answered on Likert-type scales.…”