Examining Retention Methods in Factor Analysis: A Comparison of Polychoric and Pearson Correlations for Categorical and Continuous Data.

Authors

Keywords:

Monte Carlo simulation , Cattell’s scree test , Kaiser-Guttman-1 rule , Minimum Average Partial, Parallel Analysis, Very Simple Structure

Abstract

In the last two decade, it has become clear that retention methods must utilize polychoric correlation instead of Pearson correlation to eliminate drawbacks such as underestimation of the magnitude of the relationship between latent variables that result in spurious findings (Bernstein & Teng, 1989). In the present study, the literature review will be examined and compared using Monte Carlo simulation to determine the most parsimonious method of retention for categorical data. With continuous variables, the majority of researchers still implement Cattell’s scree test (Henson & Roberts, 2006) and Kaiser-Guttman-1 rule (Velicer et al., 2000), because these procedures are the default in popular statistical packages, such as SPSS and SAS. The present study will examine two of the most accurate methods: MAP (Minimum Average Partial) and PA (Parallel Analysis) along with Very Simple Structure (VSS) with categorical variables.

Downloads

Download data is not yet available.

Author Biography

  • Sebahattin Ziyanak, University of Texas Permian Basin

    Sebahattin Ziyanak, Associate Professor of Sociology, received his B.A. degree “With Honors” from Mimar Sinan University in Istanbul, Turkey, where he was named outstanding student in sociology in 1999. Dr. Ziyanak holds a Ph.D. in sociology from the University of North Texas in 2013. He received his M.A. in sociology from the University of Houston in 2007. He is the recipient of the President's Teaching Award in 2023, from the University of Texas Permian Basin and Freddy’s Annual Student Engagement and Leadership Award, the President's Research Award in 2020, the La Mancha Society Golden Windmill Research Award in 2018, and the Outstanding Excellence in Teaching with the National Society of Leadership and Success in 2018, Outstanding Instructor Recognition in Teaching with Thank A Teacher program for Commitment to University of North Texas Student Success in 2012 and 2013. He was the University of Texas Permian Basin nominee for the Minnie PIPER Distinguished Award in 2023 and the University of Texas Regent's Outstanding Teaching Award in 2022. He was selected as a finalist for the Pearson 2023 Exemplary Teaching & Learning Award (11 finalists out of 654 nominees nationwide)

    He authored the following books: Understanding Deviance, Crime, Social Control, and the Mass Media: The Construction of Social Order (2022), The Native American Contest Powwow: Cultural Tethering Theory (2021), Political Sociology (2020), Sociological Studies of Environmental Conflict (2019), Introduction to Sociology (2019), Turkish Immigrants in the Mainstream of American Life: Theories of International Migration (2018), Analyzing Delinquency among Kurdish Adolescents: A Test of Hirschi’s Social Bonding Theory (2015), and Crossroad: A Grassroots Organization for the Homeless in Houston (2008).

    He has contributed to nineteen book chapters and has been published in a diverse range of esteemed publications, including The Qualitative Report, Elsevier's The Extractive Industries and Society Journal, Frontiers in Sociology, International Journal of Environmental Research and Public Health, and A Race Gender Class Journal.

    Furthermore, he has actively participated in community initiatives. Since 2016, he has served as a member of the Advisory Board for the Odessa Links of the Odessa Homeless Coalition. From 2018 to 2019, he held the position of President at the Peace Academy of West Texas, and he has continued his involvement as a board member since 2019.

    Dr. Ziyanak has been chosen to lead as the president of International Studies at the Southwestern Social Science Association's 104rd Annual Meeting, scheduled for April 3-5, 2025 in Las Vegas, Nevada. His research interests include delinquency, deviance, social organization, social movement, sociology of education, environmental studies, and race and ethnicity.

References

References

Basto, M., & Pereira, J. M. (2012). An SPSS R-menu for ordinal factor analysis. Journal of Statistical Software, 46(4), 1-29.

Beauducel, A. (2001). Problems with parallel analysis in data sets with oblique simple structure. Methods of Psychological Research Online, 6(2), 141–157.

Bernstein, I. H., & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evidence for multidimensionality due to item categorization. Psychological Bulletin, 105(3), 467-477.

Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York, NY: Guilford Press.

Browne, M. W. (1968). A comparison of factor analytic techniques. Psychometrika, 33(3), 267-334.

Buja, A., & Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509–540.

Carsey, T. M., & Harden, J. J. (2014). Monte Carlo Simulation and Resampling Methods for Social Science. Thousand Oaks, CA: Sage.

Cho, S. J., Li, F., & Bandalos, D. (2009). Accuracy of the parallel analysis procedure with polychoric correlations. Educational and Psychological Measurement, 69(5), 748-759.

Choi, J., Kim, S., Chen, J., & Dannels, S. (2011). A comparison of maximum likelihood and Bayesian Estimation for polychoric correlation using Monte Carlo simulation. Journal of Educational and Behavioral Statistics, 36(4), 523–549.

Comrey, A. L., & Lee, H. B. (1992). A first course in factor analysis. Hillsdale, NJ: Erlbaum.

Costello, A. B. & Osborne J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10(7). http://pareonline.net/getvn.asp?v=10&n=7

Cramer, D., & Howitt, D. L. (2004). The Sage dictionary of statistics a practical resource for students in the social sciences. Thousand Oaks, CA: Sage.

Crawford, A. V., Green, S. B., Levy, R., Lo, W. J., Scott, L., Svetina, D., & Thompson, M. S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885–901.

Cudeck, R., & MacCallum, R. C. (Eds.). (2007). Factor Analysis at 100 Historical Developments and Future Directions. Mahwah, NJ: Lawrence Erlbaum Associates.

Dinno, A. (2011). Gently clarifying the application of Horn’s parallel analysis to principal component analysis versus factor analysis. Retrieved from http://doyenne.com/Software/files/PA_for_PCA_vs_FA.pdf

Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299.

Fava, J. L., & Velicer, W. F. (1996). The effects of underextraction in factor and component analyses. Educational and Psychological Measurement, 56(6), 907–929.

Floyd, F. J., & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment, 7(3), 286-299.

Garrido, L. E., Abad, F. J., & Ponsoda, V. (2011). Performance of Velicer’s minimum average partial factor retention method with categorical variables. Educational and Psychological Measurement, 71(3), 551–570.

Garrido, L. E., Abad, F. J., & Ponsoda, V. (2013). A new look at Horn’s parallel analysis with ordinal variables. Psychological methods, 18(4), 454-475.

Glorfeld, L. W. (1995). An improvement on Horn's parallel analysis methodology for selecting the correct number of factors to retain. Educational and psychological measurement, 55(3), 377-393.

Gorsuch, R. L. (1983). Factor analysis (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates.

Gorsuch, R. L. (1997). Exploratory factor analysis: Its role in item analysis. Journal of Personality Assessment, 68(3), 532–560.

Gorsuch, R. L. (2003). Factor analysis. In J. A. Schinka & W. F. Velicer (Eds.). Handbook of psychology: Research methods in psychology (Vol. 2, pp. 143–164). John Wiley and Sons Inc.

Harwell, M., Stone, C. A., Hsu, T. C., & Kirisci, L. (1996). Monte Carlo studies in item response theory. Applied Psychological Measurement, 20(2), 101–125.

Hayton, J. C., Allen, D. G., & Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational Research Methods, 7(2), 191–205.

Henson, R. K., Capraro, R. M., & Capraro, M. M. (2004). Reporting practices and use of exploratory factor analyses in educational research journals: Errors and explanation. Research in the Schools, 11(2), 61–72.

Henson, R. K., & Roberts, J. K. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological Measurement, 66(3), 393–416.

Holgado–Tello, F. P., Chacón–Moscoso, S., Barbero–García, I., & Vila–Abad, E. (2010). Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables. Quality & Quantity, 44(1), 153-166.

Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179-185.

Hutchinson, S. R., & Bandalos, D. L. (1997). A guide to Monte Carlo simulation research for applied researchers. Journal of Vocational Education Research, 22(4), 233–245.

Lorenzo-Seva, U., & Ferrando, P. J. (2006). Factor: A computer program to fit the exploratory factor analysis model. Behavior Research Methods, Instruments, & Computers, 38(1), 88–91.

Lorenzo-Seva ,U.,Timmerman,M.E., & Kiers,H.A.L. (2011). The hull method for selecting the number of common factors. Multivariate Behavioral Research, 46(2), 340–364.

MacCallum, R.C.,Widaman, K.F., Preacher, K.J., Hong, S. (2001). Sample size in factor analysis: the role of model error. Multivariate Behavioral Research. 36(4), 611–637.

MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological methods, 4(1), 84-99.

Mooney, C. Z. (Ed.). (1997). Monte Carlo simulation. SAGE.

Mundform, D. J., Schaffer, J., Kim, M. J., Shaw, D., Thongteeraparp, A., & Supawan, P. (2011). Number of replications required in Monte Carlo simulation studies: A synthesis of four studies. Journal of Modern Applied Statistical Methods, 10(1), 19-28.

O’Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test. Behavior Research Methods, Instruments, & Computers, 32(3), 396–402.

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.

Preacher, K. J., Zhang, G., Kim, C., & Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48(1), 28–56.

Revelle, W. (2013). psych: Procedures for Personality and Psychological Research. Northwestern University, Evanston. R package version 1.3.9

Revelle, W. & Rocklin, T. (1979). Very Simple Structure - alternative procedure for

estimating the optimal number of interpretable factors. Multivariate Behavioral Research, 14(4), 403-414.

Spearman, C. (1904).“General Intelligence,” Objectively Determined and Measured. The American Journal of Psychology, 15(2), 201-292.

Stevens, J. (2002). Applied multivariate statistics for the social sciences. Taylor & Francis US.

Tabachnick, B. G., & Fidell, L. S. (2001). Using multivariate statistics. Allyn and Bacon.

Thoemmes, F., MacKinnon, D. P., & Reiser, M. R. (2010). Power analysis for complex mediational designs using Monte Carlo methods. Structural Equation Modeling, 17(3), 510-534.

Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding concepts and applications. American Psychological Association.

Timmerman, M. E., & Lorenzo-Seva, U. (2011). Dimensionality assessment of ordered polytomous items with parallel analysis. Psychological Methods, 16(2), 209-220.

Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321-327.

Velicer, W. F., Eaton, C. A., & Fava, J. L. (2000). Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. In Problems and solutions in human assessment (pp. 41-71). Springer US.

Velicer, W. F., & Jackson, D. N. (1990). Component analysis versus common factor analysis: Some issues in selecting an appropriate procedure. Multivariate behavioral research, 25(1), 1-28.

Wilcox, R. R. (1988). Simulation as a research technique. In J. P. Reeves (Ed.), Educational research, methodology, and measurement: An international handbook (pp. 134-137). Pergamon.

Wilcox, R. R. (1992). Comparing one-step M-estimators of location corresponding to two independent groups. Psychometrika, 57(1), 141–154.

Wood, J. M., Tataryn, D. J., & Gorsuch, R. L. (1996). Effects of under-and overextraction on principal axis factor analysis with varimax rotation. Psychological Methods, 1(4), 354-365.

Worthington, R. L., & Whittaker, T. A. (2006). Scale development research a content analysis and recommendations for best practices. The Counseling Psychologist, 34(6), 806–838.

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of

components to retain. Psychological bulletin, 99(3), 432-442.

Published

2024-09-04

How to Cite

Ziyanak, S., & Yagci, J. . (2024). Examining Retention Methods in Factor Analysis: A Comparison of Polychoric and Pearson Correlations for Categorical and Continuous Data. Journal of Educational Impact, 1(1), 13-34. https://journal.eduimpact.net/index.php/jei/article/view/3