Methods and Rule-of-Thumbs in The Determination of Minimum Sample Size When Appling Structural Equation Modelling: A Review
Keywords:Structural Equation Modelling., Minimum Sample Size Determination
Basic methods and techniques involved in the determination of minimum sample size at the use of Structural Equation Modeling (SEM) in a research project, is one of the crucial problems faced by researchers since there were some controversy among scholars regarding methods and rule-of-thumbs involved in the determination of minimum sample size when applying Structural Equation Modeling (SEM). Therefore, this paper attempts to make a review of the methods and rule-of-thumbs involved in the determination of sample size at the use of SEM in order to identify more suitable methods. The paper collected research articles related to the sample size determination for SEM and review the methods and rules-of-thumb employed by different scholars. The study found that a large number of methods and rules-of-thumb have been employed by different scholars. The paper evaluated the surface mechanism and rules-of-thumb of more than twelve previous methods that contained their own advantages and limitations. Finally, the study identified two methods that are more suitable in methodologically and technically which have identified by non-robust scholars who deeply addressed all the aspects of the techniques in the determination of minimum sample size for SEM analysis and thus, the prepare recommends these two methods to rectify the issue of the determination of minimum sample size when using SEM in a research project.
American Psychological Association. (2009). Publication Manual of the American Psychological Association, 6th Edition (6th ed.). American Psychological Association.
Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence improper solutions, and goodness of fit indices for Maximum likelihood conformity factor analysis. Psychometrika, 49, 155 – 172.
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–246. https://doi.org/10.1037/0033-2909.107.2.238
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606. https://doi.org/10.1037/0033-2909.88.3.588
Boomsma, A. (1985). Non- convergence, improper solutions, and starting values in LISREL maximum likelihood estimation. Psychometrika, 50, 229–242.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). L. Erlbaum Associates.
Ding, L., Velicer, W. F., & Harlow, L. L. (1995). Effects of estimation methods, number of indicators per factor, and improper solutions on structural equation modeling fit indices. Structural Equation Modeling: A Multidisciplinary Journal, 2(2), 119–143. https://doi.org/10.1080/10705519509540000
Fornell, C., & Bookstein, F. L. (1982). Two Structural Equation Models: LISREL and PLS Applied to Consumer Exit-Voice Theory. Journal of Marketing Research, 19(4), 440–452. https://doi.org/10.2307/3151718
Goodhue, D., Lewis, W., & Thompson, R. L. (2006). PLS, Small Sample Size, and Statistical Power in MIS Research. Proceedings of the 39th Annual Hawaii International Conference on System Sciences (HICSS’06). https://doi.org/10.1109/HICSS.2006.381
Goodhue, D., Lewis, W., & Thompson, R. L. (2012). Does PLS Have Advantages for Small Sample Size or Non-Normal Data? MIS Quarterly, 36(3), 981–1001. https://doi.org/10.2307/41703490
Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2014). A primer on partial Least Squares Structural Equation Modeling (PLS-SEM). Thousand Oaks, California: SAGE Publications.
Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a Silver Bullet. Journal of Marketing Theory and Practice, 19(2), 139–152. https://doi.org/10.2753/MTP1069-6679190202
Hox, J. J., & Bechger, T. M. (1999). An Introduction to Structural Equation Modelling. Family Science Review, 11, 354–373.
Kline, R. B. (1998). Methodology in the social sciences. Principles and practice of structural equation modeling. Guilford Press.
Kline, R. B. (2005). Methodology in the social sciences. Principles and practice of structural equation modeling (2nd ed.). Guilford Press.
Kock, N. (2015). One-tailed or two-tailed P values in PLS-SEM? International Journal of E-Collaboration, 11(2), 1–7.
Kock, N. (2016). Non-normality propagation among latent variables and indicators in PLS-SEM simulations. Journal of Modern Applied Statistical Methods, 15(1), 299–315.
Kock, N., & Hadaya, P. (2018). Minimum sample size estimation in PLS‐SEM: The inverse square root and gamma‐exponential methods. Information Systems Journal, 28(1), 227–261.
Kock, N., & Lynn, G. S. (2012). Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations. Journal of the Association for Information Systems, 13(7), 546–580.
MacCallum, R. C., & Austin, J. T. (2000). Application of structural equation modeling in psychological research. Annual Review of Psychology, 51, 201–226.
MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4, 84–99.
Marcoulides, G. A., & Chin, W. W. (2013). You write, but others read: Common methodological mis-understandings in PLS and related methods. In New perspectives in partial least squares and related methods (pp. 31–64). Springer, New York, NY.
Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103(3), 391–410. https://doi.org/10.1037/0033-2909.103.3.391
Miaoulis, G., & Michener, R. D. (1976). An Introduction to Sampling. Kendall/Hunt Publishing Company: Dubuque, Iowa.
Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S., & Stilwell, C. D. (1989). Evaluation of goodness-of-fit indices for structural equation models. Psychological Bulletin, 105(3), 430–445. https://doi.org/10.1037/0033-2909.105.3.430
Muthén, L. K., & Muthén, B. O. (2002). How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power. Structural Equation Modeling: A Multidisciplinary Journal, 9(4), 599–620. https://doi.org/10.1207/S15328007SEM0904_8 Nunnally, J. C. (1967). Psychometric theory. McGraw-Hill.
Paxton, P., Curran, P. J., Bollen, K. A., Kirby, J., & Chen, F. (2001). Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8(2), 287–312. https://doi.org/10.1207/S15328007SEM0802_7
Raykov, T. (2006). A first course in structural equation modeling (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
Ringle, C. M., Sarstedt, M., & Straub, D. W. (2012). Editor’s comments: A critical look at the use of PLS-SEM in MIS quarterly. 36(1). https://doi.org/10.2307/41410402
Robert, C., & Casella, G. (1999). Monte Carlo Statistical Methods. Springer-Verlag. https://doi.org/10.1007/978-1-4757-3071-5
Sarstedt, M., Ringle, C. M., & Hair, J. F. (2017). Partial Least Squares Structural Equation Modeling (In: Homburg C., Klarmann M., Vomberg A. (Eds). Handbook of Market Research, Heidelberg: Springer.
Singh, A. S., & Masuku, M. B. (2014). Sampling techniques & determination of sample size in applied statistics research: An overview. International Journal of Economics, Commerce and Management, Vol II (Issue 11).
Tanaka, J. S. (1987). How big is enough? Sample size and goodness-of-fit in structural equation models with latent variables. Child Development, S8, 134 – 146.
Velicer, W. F., & Fava, J. L. (1998). Affects of variable and subject sampling on factor pattern recovery. Psychological Methods, 3(2), 231–251. https://doi.org/10.1037/1082-989X.3.2.231
Weakliem, D. L. (2016). Hypothesis Testing and Model Selection in the Social Sciences (1 edition). The Guilford Press.
Westland, J. C. (2010). Lower bounds on sample size in structural equation modeling. Electronic Commerce Research and Applications, 9, 476– 487. https://doi.org/10.1016/j.elerap.2010.07.003
Wilkinson, L. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604. https://doi.org/10.1037/0003-066X.54.8.594
Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample Size Requirements for Structural Equation Models: An Evaluation of Power, Bias, and Solution Propriety. Educational and Psychological Measurement, 76(6), 913–934. https://doi.org/10.1177/0013164413495237
How to Cite
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.