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The Scree Test and the Number of Factors: a Dynamic Graphics Approach

Published online by Cambridge University Press:  17 March 2015

Rubén Daniel Ledesma ,
Pedro Valero-Mora  and
Guillermo Macbeth
Rubén Daniel Ledesma*
Affiliation:
Universidad Nacional de Mar del Plata (Argentina)
Pedro Valero-Mora
Affiliation:
Universidad de Valencia (Spain)
Guillermo Macbeth
Affiliation:
Universidad Nacional de Entre Ríos (Argentina)
*
*Correspondence concerning this article should be addressed to Ruben D. Ledesma. Universidad Nacional de Mar del Plata & Consejo Nacional de Investigaciones Científicas y Técnicas. Rio Negro, 3922. 7600. Mar del Plata (Argentina). E-mail. rdledesma@conicet.gov.ar
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Abstract

Exploratory Factor Analysis and Principal Component Analysis are two data analysis methods that are commonly used in psychological research. When applying these techniques, it is important to determine how many factors to retain. This decision is sometimes based on a visual inspection of the Scree plot. However, the Scree plot may at times be ambiguous and open to interpretation. This paper aims to explore a number of graphical and computational improvements to the Scree plot in order to make it more valid and informative. These enhancements are based on dynamic and interactive data visualization tools, and range from adding Parallel Analysis results to "linking" the Scree plot with other graphics, such as factor-loadings plots. To illustrate our proposed improvements, we introduce and describe an example based on real data on which a principal component analysis is appropriate. We hope to provide better graphical tools to help researchers determine the number of factors to retain.

Keywords

factor analysisscree testdata visualization
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 18 , 2015 , E11
Copyright
Copyright © Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2015 

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References

Beauducel, A. (2001). Problems with parallel analysis in data sets with oblique simple structure. Methods of Psychological Research Online, 6, 141–157.Google Scholar
Becker, R. A., Cleveland, W. S., & Wilks, A. R. (1987). Dynamic graphics for data analysis. Statistical Science, 2, 355–383. http://dx.doi.org/10.1214/ss/1177013104 Google Scholar
Buja, A., & Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27, 509–540. http://dx.doi.org/10.1207/s15327906mbr2704_2 CrossRefGoogle ScholarPubMed
Cattell, R. B. (1966). The Scree test for the number of factors. Multivariate Behavioral Research, 1, 245–276. http://dx.doi.org/10.1207/s15327906mbr0102_10 Google Scholar
Cattell, R. B., & Vogelman, S. (1977). A comprehensive trial of the scree and KG criteria for determining the number of factors. Multivariate Behavioral Research, 12, 289–325. http://dx.doi.org/10.1207/s15327906mbr1203_2 Google Scholar
Cleveland, W. S., & McGill, M. E. (1988). Dynamic graphics for statistics. Belmont, CA: Wadsworth.Google Scholar
Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment Research & Evaluation, 10, 7.Google Scholar
Cota, A. A., Longman, R. S., Holden, R. R., Fekken, G. C., & Xinaris, S. (1993). Interpolating 95th percentile eigenvalues from random data: An empirical example. Educational & Psychological Measurement, 53, 585–596. http://dx.doi.org/10.1177/0013164493053003001 Google Scholar
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, 272–299. http://dx.doi.org/10.1037//1082-989X.4.3.272 Google Scholar
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, 377–393. http://dx.doi.org/10.1177/0013164495055003002 CrossRefGoogle Scholar
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, 191–205. http://dx.doi.org/10.1177/1094428104263675 Google Scholar
Hong, S., Mitchell, S. K., & Harshman, R. A. (2006). Bootstrap Scree Tests: A Monte Carlo simulation and applications to published data. British Journal of Mathematical and Statistical Psychology, 59, 35–57. http://dx.doi.org/10.1348/000711005X66770 Google Scholar
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179–185. http://dx.doi.org/10.1007/BF02289447 Google Scholar
Horn, J. L., & Engstrom, R. (1979). Cattell's Scree Test in relation to Bartlett's chi-square test and other observations on the number of factors problem. Multivariate Behavioral Research, 14, 283–300. http://dx.doi.org/10.1207/s15327906mbr1403_1 Google Scholar
Humphreys, L. G., & Montanelli, R. G. (1975). An investigation of the parallel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 10, 193–206. http://dx.doi.org/10.1207/s15327906mbr1002_5 CrossRefGoogle Scholar
Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141–151. http://dx.doi.org/10.1177/001316446002000116 Google Scholar
Keeling, K. B. (2000). A regression equation for determining the dimensionality of data. Multivariate Behavioral Research, 35, 457–468. http://dx.doi.org/10.1207/S15327906MBR3504_02 Google Scholar
Lautenschlager, G. J. (1989). A comparison of alternatives to conducting Monte Carlo analyses for determining parallel analysis criteria. Multivariate Behavioral Research, 24, 365–395. http://dx.doi.org/10.1207/s15327906mbr2403_6 CrossRefGoogle ScholarPubMed
Lautenschlager, G. J., Lance, C. E., & Flaherty, V. L. (1989). Parallel analysis criteria: Revised regression equations for estimating the latent roots of random data correlation matrices. Educational and Psychological Measurement, 49, 339–345. http://dx.doi.org/10.1177/0013164489492006 Google Scholar
Ledesma, R., & Valero-Mora, P. (2007). Determining the number of factors to retain in EFA: An easy-to-use computer program for carrying out Parallel Analysis. Practical Assessment, Research & Evaluation, 12, 1.Google Scholar
Ledesma, R. D., Molina, J. G., Young, F. W., & Valero-Mora, P. M. (2007). Desarrollo de técnicas de visualización múltiple en el programa ViSta: Ejemplo de aplicación al Análisis de Componentes Principales [Developing multiple-visualization techniques in ViSta. The case of Principal Component Analysis]. Psicothema, 19, 497–505.Google Scholar
Longman, R. S., Cota, A. A., Holden, R. R., & Fekken, G. C. (1989). A regression equation for the parallel analysis criterion in principal components analysis: Mean and 95th percentile eigenvalues. Multivariate Behavioral Research, 24, 59–69. http://dx.doi.org/10.1207/s15327906mbr2401_4 CrossRefGoogle ScholarPubMed
Molina, J. G., Ledesma, R. D, Valero-Mora, P., & Young, F. W. (2005). A video tour through ViSta 6.4, a visual statistical system based on Lisp-Stat. Journal of Statistical Software 13, 1–13.Google Scholar
Raîche, G., Walls, T. A., Magis, D., Riopel, M., & Blais, J. G (2013). Non-graphical solutions for Cattell’s scree test. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9, 23–29. http://dx.doi.org/10.1027/1614-2241/a000051 Google Scholar
Taubman-Ben-Ari, O., Mikulincer, M., & Gillath, O. (2004). The multidimensional driving style inventory-scale construct and validation. Accident Analysis and Prevention, 36, 323–332. http://dx.doi.org/10.1016/S0001-4575(03)00010-1 Google Scholar
Tierney, L. (1990). Lisp-stat an object-oriented environment for statistical computing and dynamic graphics. New York, NY: John Wiley & Sons.Google Scholar
Turner, N. E. (1998). The effect of common variance and structure pattern on random data eigenvalues: Implications for the accuracy of parallel analysis. Educational and Psychological Measurement, 58, 541–568. http://dx.doi.org/10.1177/0013164498058004001 Google Scholar
Valero-Mora, P., Ledesma, R. D, & Friendly, M. (2012). The history of ViSta: The visual statistics system. Wiley Interdisciplinary Reviews: Computational Statistics, 4, 295–306. http://dx.doi.org/10.1002/wics.1203 Google Scholar
Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41, 321–327. http://dx.doi.org/10.1007/BF02293557 Google Scholar
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 Goffin, R. D., & Helmes, E. (Eds.), Problems and solutions in human assessment: Honoring Douglas N. Jackson at seventy (pp. 41–71). Boston, MA: Kluwer.Google Scholar
Velicer, W. F., & Jackson, D. N. (1990). Component analysis versus common factor analysis: Some further observations. Multivariate Behavioral Research, 25, 97–114. http://dx.doi.org/10.1207/s15327906mbr2501_12 CrossRefGoogle ScholarPubMed
Young, F. W. (1996). ViSta: Developing statistical objects. [Memorandum]. Chapel Hill, NC: Thurstone Psychometric Lab, University of North Carolina.Google Scholar
Young, F. W., Valero-Mora, P., Faldowski, R., & Bann, C. M. (2003). Gossip: The architecture of spreadplots. Journal of Computational and Graphical Statistics, 12, 80–100. http://dx.doi.org/10.1198/1061860031356 CrossRefGoogle Scholar
Young, F. W., Valero-Mora, P., & Friendly, M. (2006). Visual statistic: Seeing data with dynamic interactive graphics. Hoboken, NJ: John Wiley and Sons.CrossRefGoogle Scholar
Yu, C. H., Popp, S. O., DiGangi, S., & Jannasch-Pennell, A. (2007). Assessing unidimensionality: A comparison of Rasch Modeling, Parallel Analysis, and TETRAD. Practical Assessment Research & Evaluation, 12, 14.Google Scholar
Zwick, W. R., & Velicer, W. F. (1982). Factors influencing four rules for determining the number of components to retain. Multivariate Behavioral Research, 17, 253–269. http://dx.doi.org/10.1207/s15327906mbr1702_5 Google Scholar
Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432–442. http://dx.doi.org/10.1037/0033-2909.99.3.432 Google Scholar