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Have your cake and eat it too: PLSe2 = ML + PLS

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Abstract

PLSe1 and PLSe2 methods were developed in 2013. While the performance of PLSe1 under normality and non-normality conditions has been confirmed, the performance of PLSe2, proposed to provide an avenue for the resurrection of PLS as a fully justified statistical methodology, has not yet been verified under non-normality condition. For this reason, our study aims at testing the performance of PLSe2 with non-normal data based on a Monte Carlo simulation using a simple and a complex model. In addition, it aims at providing a step-by-step visual guideline on how to apply this method in estimating a simple mediation model using EQS 6.4. The results of the Monte Carlo simulations across different numbers of replications and sample sizes provided substantial support for the performance of PLSe2 under non-normality conditions since the produced estimates were unbiased and virtually identical to the parameters resulted from the traditional ML estimation. In addition, we provided evidence about the suitability of different robust test statistics for the purpose of model evaluation based on our simulation results. Regarding the empirical example, we estimated a mediation model using ML, PLSe2, and PLSc estimators, compared the results across these methods, and provided further support for our PLSe2 and ML results through running a resampling bootstrap simulation. Overall, while we empirically validated the PLSe2 method using Monte Carlo simulations, our findings suggest that PLSe2 has the advantages of both ML and PLS and performs well under non-normality (and normality) conditions, thereby suggesting it as the methodology of choice for model specification, estimation, and evaluation in social sciences empirical studies.

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Data availability

The data that support the findings of the empirical example in this study are openly available in HARVARD DATAVERSE at https://doi.org/10.7910/DVN/TNGALP.

Notes

  1. In the measurement model displayed in matrix format, ηi are factors; λi,j are factor loadings; yi are equations for the items; and εi are the residuals of the equations.

  2. In the structural model displayed in matrix format, ηi are factors; βi,j are path coefficients; and ζi are disturbance terms of the equations.

  3. EQS supports model-based and resampling bootstrap simulations (Bentler 2006). The procedure of running the resampling bootstrap simulations has not been illustrated as they were not the core objective of this study. However, no convergence problems occurred in the replications (100% success with no condition code).

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Acknowledgements

We appreciate the support of our families to finish this manuscript during unprecedented global crises and workplace upheaval. We also are indebted to the editor and review team for their efforts and contributions during this time. Similarly, we appreciate the responsive support of the technical team at Multivariate Software Inc. (www.mvsoft.com). A part of this project was presented at International Symposium on Applied Structural Equation Modeling and Methodological Matters (SASEM) 2019, Melaka, Malaysia.

Funding

This research study was supported by the Universiti Sains Malaysia (Grant Number: 304/CIPPTN/6315200).

Author information

Authors and Affiliations

  1. National Higher Education Research Institute (IPPTN), Universiti Sains Malaysia (USM), Bayan Lepas, Penang, Malaysia

    Majid Ghasemy & Hazri Jamil

  2. Marriott School of Business, Brigham Young University, Provo, UT, USA

    James E. Gaskin

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  1. Majid Ghasemy
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Appendices

Appendix A

The univariate skewness and kurtosis statistics of the items of the simulated 2-factor CFA model under the non-normality condition.

Item

Skewness

Kurtosis

λ1,1

− 1.75

4.00

λ2,1

1.50

2.50

λ3,1

− 1.50

4.35

λ4,2

1.00

2.50

λ5,2

− 0.90

3.00

λ6,2

1.50

2.50

Appendix B

The univariate skewness and kurtosis statistics of the items of the simulated non-recursive model under the non-normality condition.

Item

Skewness

Kurtosis

λ1,1

− 1.50

3.00

λ2,1

1.50

2.50

λ3,1

− 1.00

3.35

λ4,2

1.00

2.50

λ5,2

− 0.60

2.70

λ6,3

1.50

2.50

λ7,3

− 1.20

2.70

λ8,3

− 1.00

1.65

λ9,4

− 0.10

2.35

λ10,4

0.30

2.60

λ11,5

− 0.70

3.30

λ12,5

− 0.60

3.20

λ13,5

1.50

3.80

Appendix C

The *.eqs file to verify the performance of ML under the non-normality condition (N = 3000, Replication = 1000).

figure a

Appendix D

The *.eqs file to verify the performance of PLSe2 under the non-normality condition (N = 3000, Replication = 1000).

figure b

Appendix E

The items of the final model of the empirical example

Construct

Code

Item

Creating value for the community

CVC1

I emphasize the importance of giving back to the community

CVC2

I am always interested in helping people in the community

CVC3

I am involved in community activities

CVC4

I encourage others to volunteer in the community

Job performance

JP6

When I want to reach a goal, I am usually able to succeed

JP7

I complete work in a timely and effective manner

JP8

I complete a large quantity of work

JP9

I perform high-quality work

Job satisfaction

JS2

I feel close to the people at work

JS3

I feel good about working at this institution

JS4

I feel secure about my job

JS5

I believe management is concerned about me

JS9

I get along with my supervisors

JS10

I feel good about my job

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Ghasemy, M., Jamil, H. & Gaskin, J.E. Have your cake and eat it too: PLSe2 = ML + PLS. Qual Quant 55, 497–541 (2021). https://doi.org/10.1007/s11135-020-01013-6

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