The Precision of the Overall Data-Model Fit for Different Design Features in Confirmatory Factor Analysis

  • D. Almaleki Department of Evaluation, Measurement, and Research, Umm Al-Qura University, Saudi Arabia
Volume: 11 | Issue: 1 | Pages: 6766-6774 | February 2021 |


Factor Analysis (FA) is the study of variance within a group. Within-Subject Variance (WSV) is affected by multiple features in a study context such as the Experimental Design (ED) or the Sampling Design (SD). The aim of this study is to provide an empirical evaluation of the influence of different aspects of ED and SD on WSV in the context of FA in terms of model precision. The study results showed that the precisions of the overall model fit indices TLI and CFI, as functions of VTF, STV, h2, and their interaction, varied, as did the precisions of the overall model fit indices GFI, AGFI, and RMSEA as functions of VTF, STV, and their interactions. Overall, when the VTF is 4:1 or 7:1, the required STV is 16:1 or above 32:1 or above to show precision in factor solution.

Keywords: model-precision, factor-analysis, model-fit, model-design


Download data is not yet available.


L. Crocker and J. Algina, Introduction to Classical and Modern Test Theory. Bristol , UK: ERIC, 1986.

A. B. Costello and J. Osborne, "Best practices in exploratory factor analysis ; four recommendations for getting the most from your analysis," Practical Assessment, Research, and Evaluation, vol. 10, no. 10, 2005, Art. no. 7.

T. A. Brown, Confirmatory Factor Analysis for Applied Research, Second edition. London, UK: The Guilford Press, 2015.

F. B. Bryant and P. R. Yarnold, "Principal-components analysis and exploratory and confirmatory factor analysis," in Reading and understanding multivariate statistics, Washington, DC, US: American Psychological Association, 1995, pp. 99-136.

I. P. Cobham, "The effects of subject-to-variable ratio, measurement scale, and number of factors on the stability of the factor model," Ph.D. dissertation, University of Miami, FL, USA, 1999.

L. Hatcher, A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modeling, 1st edition. North Carolina, USA: SAS Publishing, 1994.

K. Coughlin, "An Analysis of Factor Extraction Strategies: A Comparison of the Relative Strengths of Principal Axis, Ordinary Least Squares, and Maximum Likelihood in Research Contexts that Include both Categorical and Continuous Variables," Ph.D. dissertation, University of South Florida, FL, USA, 2013.

L. R. Goldberg, "The development of markers for the Big-Five factor structure," Psychological Assessment, vol. 4, no. 1, pp. 26-42, 1992.

D. L. Bandalos and P. Gagne, "Simulation methods in structural equation modeling," in Handbook of structural equation modeling, New York, USA: The Guilford Press, 2012, pp. 92-108.

H.-M. Lin, M.-H. Lee, J.-C. Liang, H.-Y. Chang, P. Huang, and C.-C. Tsai, "A review of using partial least square structural equation modeling in e-learning research," British Journal of Educational Technology, vol. 51, no. 4, pp. 1354-1372, 2020.

L. Fabrigar, D. Wegener, R. MacCallum, and E. Strahan, "Evaluating the Use of Exploratory Factor Analysis in Psychological Research," Psychological Methods, vol. 4, no. 3, pp. 272-299, Sep. 1999.

Y. A. Wang and M. Rhemtulla, "Power Analysis for Parameter Estimation in Structural Equation Modeling:A Discussion and Tutorial," in Advances in Methods and Practices in Psychological Science, California, USA: University of California, 2020.

M. J. Allen, Introduction to measurement theory. CA, USA: Cole Publishing, 1979.

K. M. Marcoulides, N. Foldnes, and S. Gr√łnneberg, "Assessing Model Fit in Structural Equation Modeling Using Appropriate Test Statistics," Structural Equation Modeling: A Multidisciplinary Journal, vol. 27, no. 3, pp. 369-379, May 2020.

Y. Rosseel, "Small sample solutions for structural equation modeling," in Small Sample Size Solutions, London, UK: Routledge, 2020, pp. 226-238.

S. C. Smid, D. McNeish, M. Miocevic, and R. van de Schoot, "Bayesian Versus Frequentist Estimation for Structural Equation Models in Small Sample Contexts: A Systematic Review," Structural Equation Modeling: A Multidisciplinary Journal, vol. 27, no. 1, pp. 131-161, Jan. 2020.

S. Zitzmann and M. Hecht, "Going Beyond Convergence in Bayesian Estimation: Why Precision Matters Too and How to Assess It," Structural Equation Modeling: A Multidisciplinary Journal, vol. 26, no. 4, pp. 646-661, Jul. 2019.

E. Guadagnoli and W. F. Velicer, "Relation of sample size to the stability of component patterns," Psychological Bulletin, vol. 103, no. 2, pp. 265-275, 1988.

J. C. Westland, "Lower bounds on sample size in structural equation modeling," Electronic Commerce Research and Applications, vol. 9, no. 6, pp. 476-487, Nov. 2010.

P. F. M. Bullon, "Failing to replicate: Hypothesis testing as a crucial key to make direct replications more credible and predictable," Ph.D. dissertation, Western Michigan University, MC, USA, 2015.

O. P. John and S. Srivastava, "The Big Five Trait taxonomy: History, measurement, and theoretical perspectives," in Handbook of personality: Theory and research, New York, NY, USA: Guilford Press, 1999, pp. 102-138.

J. Wang and X. Wang, Structural Equation Modeling: Applications Using Mplus, 2nd edition. New York, NY, USA: Wiley, 2019.

D. L. Moody, "The method evaluation model: a theoretical model for validating information systems design methods," in 11th European Conference on Information Systems, Naples, Italy, Jun. 2003, pp. 1-17, Accessed: Jan. 21, 2021.

L. H. Lam, T. D. H. Phuc, and N. H. Hieu, "Simulation Models For Three-Phase Grid Connected PV Inverters Enabling Current Limitation Under Unbalanced Faults," Engineering, Technology & Applied Science Research, vol. 10, no. 2, pp. 5396-5401, Apr. 2020.

A. H. Blasi and M. Alsuwaiket, "Analysis of Students' Misconducts in Higher Education using Decision Tree and ANN Algorithms," Engineering, Technology & Applied Science Research, vol. 10, no. 6, pp. 6510-6514, Dec. 2020.

R. O. Mueller and G. R. Hancock, "Structural Equation Modeling," in The Reviewer's Guide to Quantitative Methods in the Social Sciences, London, UK: Routledge, 2018, pp. 445-456.

M. K. Cain and Z. Zhang, "Fit for a Bayesian: An Evaluation of PPP and DIC for Structural Equation Modeling," Structural Equation Modeling: A Multidisciplinary Journal, vol. 26, no. 1, pp. 39-50, Jan. 2019.

J. S. Tanaka, "'How Big Is Big Enough?': Sample Size and Goodness of Fit in Structural Equation Models with Latent Variables," Child Development, vol. 58, no. 1, pp. 134-146, 1987.

K. H. Kim and P. M. Bentler, "Data Modeling: Structural Equation Modeling," in Handbook of complementary methods in education research, J. L. Green, G. Camilli, and P. B. Elmore, Eds. Mahwah, NJ, USA: Lawrence Erlbaum Associates, 2006, pp. 161-175.

B. O. Muthen and A. Satorra, "Complex Sample Data in Structural Equation Modeling," Sociological Methodology, vol. 25, pp. 267-316, 1995.

K. Y. Hogarty, C. V. Hines, J. D. Kromrey, J. M. Ferron, and K. R. Mumford, "The Quality of Factor Solutions in Exploratory Factor Analysis: The Influence of Sample Size, Communality, and Overdetermination," Educational and Psychological Measurement, vol. 65, no. 2, pp. 202-226, Apr. 2005.

A. J. S. Morin, N. D. Myers, and S. Lee, "Modern Factor Analytic Techniques," in Handbook of Sport Psychology, New York, NY, USA: John Wiley & Sons, 2020, pp. 1044-1073.

B. S. Everitt, "Multivariate Analysis: The Need for Data, and other Problems," The British Journal of Psychiatry, vol. 126, no. 3, pp. 237-240, Mar. 1975.

G. D. Garson, Factor Analysis. NC, USA: Statistical Associates Publishers, 2013.

C. M. Ringle, M. Sarstedt, R. Mitchell, and S. P. Gudergan, "Partial least squares structural equation modeling in HRM research," The International Journal of Human Resource Management, vol. 31, no. 12, pp. 1617-1643, Jul. 2020.

B. Thompson, "Ten commandments of structural equation modeling," in Reading and understanding MORE multivariate statistics, Washington, DC, US: American Psychological Association, 2000, pp. 261-283.

R. K. Henson and J. K. Roberts, "Use of Exploratory Factor Analysis in Published Research: Common Errors and Some Comment on Improved Practice," Educational and Psychological Measurement, vol. 66, no. 3, pp. 393-416, Jun. 2006.

A. H. Soomro, A. S. Larik, M. A. Mahar, A. A. Sahito, and I. A. Sohu, "Simulation-based Analysis of a Dynamic Voltage Restorer under Different Voltage Sags with the Utilization of a PI Controller," Engineering, Technology & Applied Science Research, vol. 10, no. 4, pp. 5889-5895, Aug. 2020.

D. Almaleki, "Empirical Evaluation of Different Features of Design in Confirmatory Factor Analysis," Ph.D. dissertation, Western Michigan University, MC, USA, 2016.

C. Wardley, E. Applegate, A. Almaleki, and J. V. Rhee, "Is Student Stress Related to Personality or Learning Environment in a Physician Assistant Program?," The Journal of Physician Assistant Education, vol. 30, no. 1, pp. 9-19, Mar. 2019.

C. S. Wardley, E. B. Applegate, A. D. Almaleki, and J. A. Van Rhee, "A Comparison of Students' Perceptions of Stress in Parallel Problem-Based and Lecture-Based Curricula," The Journal of Physician Assistant Education, vol. 27, no. 1, pp. 7-16, Mar. 2016.

A. W. Meade and D. J. Bauer, "Power and Precision in Confirmatory Factor Analytic Tests of Measurement Invariance," Structural Equation Modeling: A Multidisciplinary Journal, vol. 14, no. 4, pp. 611-635, Oct. 2007.

S. V. Paunonen and D. N. Jackson, "What Is Beyond the Big Five? Plenty!," Journal of Personality, vol. 68, no. 5, pp. 821-835, 2000.


Abstract Views: 441
PDF Downloads: 201

Metrics Information
Bookmark and Share

Most read articles by the same author(s)