Advertisement

Behavior Research Methods

, Volume 47, Issue 3, pp 884–889 | Cite as

POLYMAT-C: a comprehensive SPSS program for computing the polychoric correlation matrix

  • Urbano Lorenzo-SevaEmail author
  • Pere J. Ferrando
Article

Abstract

We provide a free noncommercial SPSS program that implements procedures for (a) obtaining the polychoric correlation matrix between a set of ordered categorical measures, so that it can be used as input for the SPSS factor analysis (FA) program; (b) testing the null hypothesis of zero population correlation for each element of the matrix by using appropriate simulation procedures; (c) obtaining valid and accurate confidence intervals via bootstrap resampling for those correlations found to be significant; and (d) performing, if necessary, a smoothing procedure that makes the matrix amenable to any FA estimation procedure. For the main purpose (a), the program uses a robust unified procedure that allows four different types of estimates to be obtained at the user’s choice. Overall, we hope the program will be a very useful tool for the applied researcher, not only because it provides an appropriate input matrix for FA, but also because it allows the researcher to carefully check the appropriateness of the matrix for this purpose. The SPSS syntax, a short manual, and data files related to this article are available as Supplemental materials that are available for download with this article.

Keywords

Polychoric correlation Graded-response items Factor analysis Graded response model 

Notes

Acknowledgments

The research was partially supported by a grant from the Catalan Ministry of Universities, Research and the Information Society (2009SGR1549; 2014SGR73) and by a grant from the Spanish Ministry of Education and Science (PSI2011-22683), with the collaboration of the European Fund for the Development of Regions.

Supplementary material

13428_2014_511_MOESM1_ESM.pdf (821 kb)
ESM 1 (PDF 821 kb)
13428_2014_511_MOESM2_ESM.spv (30 kb)
ESM 2 (SPV 30 kb)
13428_2014_511_MOESM3_ESM.spv (30 kb)
ESM 3 (SPV 30 kb)
13428_2014_511_MOESM4_ESM.sps (487 kb)
ESM 4 (SPS 487 kb)
13428_2014_511_MOESM5_ESM.sps (0 kb)
ESM 5 (SPS 0 kb)
13428_2014_511_MOESM6_ESM.sav (2 kb)
ESM 6 (SAV 1 kb)
13428_2014_511_MOESM7_ESM.sav (1 kb)
ESM 7 (SAV 1 kb)

References

  1. Basto, M., & Pereira, J. M. (2012). An SPSS R-Menu for ordinal factor analysis. Journal of Statistical Software, 46(4), 1–29.Google Scholar
  2. Bollen, K. A., & Stine, R. A. (1992). Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods and Research, 21, 205–229.CrossRefGoogle Scholar
  3. Chen, J., & Choi, J. (2009). A comparison of maximum likelihood and expected a posteriori estimation for polychoric correlation using Monte Carlo simulation. Journal of Modern Applied Statistical Methods, 8, 337–354.Google Scholar
  4. 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, 523–549. doi: 10.3102/1076998610381398 CrossRefGoogle Scholar
  5. Courtney, R., & Gordon, M. (2013). Determining the number of factors to retain in EFA: Using the SPSS R-Menu v2.0 to make more judicious estimations. Practical Assessment, Research and Evaluation, 18(8), 1–13.Google Scholar
  6. Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. (1975). Robust estimation and outlier detection with correlation coefficients. Biometrika, 62, 531–545.CrossRefGoogle Scholar
  7. Einspruch, E. L. (2003). Next steps with SPSS. Thousand Oaks, CA: Sage.Google Scholar
  8. Ferrando, P. J. (2009). Difficulty, discrimination and information indices in the linear factor-analytic model for continuous responses. Applied Psychological Measurement, 33, 9–24.CrossRefGoogle Scholar
  9. Hall, P., & Martin, M. A. (1988). On bootstrap resampling and iteration. Biometrika, 75, 661–671.CrossRefGoogle Scholar
  10. Hofstee, W. K. B., Ten Berge, J. M. F., & Hendriks, A. A. J. (1998). How to score questionnaires. Personality and Individual Differences, 25, 897–909. doi: 10.1016/S0191-8869(98)00086-5 CrossRefGoogle Scholar
  11. Knol, D. L., & Berger, M. P. F. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457–477. doi: 10.1207/s15327906mbr2603_5 CrossRefGoogle Scholar
  12. Lee, C.-T., Zhang, G., & Edwards, M. C. (2012). Ordinary least squares estimation of parameters in exploratory factor analysis with ordinal data. Multivariate Behavioral Research, 47, 314–339. doi: 10.1080/00273171.2012.658340 CrossRefGoogle Scholar
  13. Lorenzo-Seva, U., & Ferrando, P. J. (2012). TETRA-COM: A comprehensive SPSS program for estimating the tetrachoric correlation. Behavior Research Methods, 44, 1191–1196. doi: 10.3758/s13428-012-0200-6 CrossRefPubMedGoogle Scholar
  14. Lorenzo-Seva, U., & Ferrando, P. J. (2013). FACTOR 9.2: A comprehensive program for fitting exploratory and semiconfirmatory factor analysis and IRT models. Applied Psychological Measurement, 37, 497–498.CrossRefGoogle Scholar
  15. Lorenzo-Seva, U., & Ferrando, P. J. (2013b). Manual of the program FACTOR (Technical Report). Universitat Rovira i Virgili, Department of Psychology. Retrieved from http://psico.fcep.urv.cat/utilitats/factor/
  16. McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Erlbaum.Google Scholar
  17. Muthén, B. (1993). Goodness of fit with categorical and other nonnormal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–234). Newbury Park, CA: Sage.Google Scholar
  18. Norusis, N. J. (1988). The SPSS guide to data analysis for SPSS/PC+. Chicago IL: SPSS.Google Scholar
  19. Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443–460. doi: 10.1007/BF02296207 CrossRefGoogle Scholar
  20. Peters, C. C., & van Voorhis, W. R. (1940). Statistical procedures and the mathematical bases. New York, NY: McGraw-Hill.CrossRefGoogle Scholar
  21. Rigdon, E. E. (2010). Polychoric correlation coefficient. In N. Salkind (Ed.), Encyclopedia of research design (pp. 1046–1049). Thousand Oaks, CA: Sage.Google Scholar
  22. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika(Monograph No. 17). Iowa City, IA: Psychometric Society.Google Scholar
  23. Schenker, N. (1985). Qualms about bootstrap confidence intervals. Journal of the American Statistical Association, 80, 360–361.CrossRefGoogle Scholar
  24. Sievers, W. (1996). Standard and bootstrap confidence intervals for the correlation coefficient. British Journal of Mathematical and Statistical Psychology, 49, 381–396.CrossRefGoogle Scholar
  25. Vigil-Colet, A., Morales-Vives, F., Camps, E., Tous, J., & Lorenzo-Seva, U. (2013). Development and validation of the Overall Personality Assessment Scale (OPERAS). Psicothema, 25, 100–106. doi: 10.7334/psicothema2011.411 PubMedGoogle Scholar
  26. Wothke, W. (1993). Nonpositive definite matrices in structural models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 256–293). Newbury Park, CA: Sage.Google Scholar

Copyright information

© Psychonomic Society, Inc. 2014

Authors and Affiliations

  1. 1.Universitat Rovira i VirgiliTarragonaSpain
  2. 2.Departament de Psicologia, Centre de Reçerca en Avalució i Mesura de la ConductaUniversitat Rovira i VirgiliTarragonaSpain

Personalised recommendations