Modelos complementarios al Análisis Factorial en la construcción de escalas ordinalesun ejemplo aplicado a la medida del Clima Social del Aula

  1. López González, Emelina
  2. Pérez Carbonell, Amparo
  3. Ramos Santana, Genoveva
Journal:
Revista de educación

ISSN: 0034-8082

Year of publication: 2011

Issue Title: La formación práctica de estudiantes universitarios: repensando el Practicum

Issue: 354

Pages: 301-302

Type: Article

DOI: 10.4438/1988-592X-RE-2011-354-004 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista de educación

Abstract

It is well known that factor analysis (FA) by principal components is one of the statistical models more frequently used in educational research to study the properties of scales of measurement. The generalised use of FA extends also to non-metric scales (such as categorical and ordinal scales), yet the properties of such scales do not meet the requirements of factor analysis (such as normal distributions and linear relationships between variables). Several problems are thus generated, but there are a number of techniques for solving to some extent the imperfect application of the FA model to nonmetric data. Some of the most important models are briefly described: parallel analysis or factor analysis using item response theory. The joint use of multivariate models of interdependence for dimensionality reduction, such as non-linear principal component analysis (NLPCA), non-metric multidimensional scaling (NM-MDS) and cluster analysis (CA), is proposed as a possible solution, because all these models can be considered appropriate for use with ordinal scales. An example of the combined, complementary use of NM-MDS and CA is shown, together with FA by principal components, to study a Likert scale concerning classroom social climate that was prepared in a prior research project. The results show that the models are significantly more fit for the data, and the internal dimension solution is more parsimonious and consistent with the underlying idea that lay at the origin of the scale.

Bibliographic References

  • Arce, C. y Andrade, E. M. (2000). Recuperación de información métrica a partir de información no-métrica con diseños de escalamiento multidimensional incompletos. Psicothema, 12, 308-313.
  • Bartholomew, D. J. (2007). Three faces of factor analysis. En R. Cudeck & R. C. Maccallum (Eds.), Factor analysis at 100. Historical development and future directions (pp. 9-21). Mahwah, NJ: LEA.
  • Bartholomew, D. J., Steele, F., Moustaki, I. & Galbrain, J. I. (2002). The analysis and interpretation of multivariate data for social scientists. Boca Raton, FL.: Chapman & Hall/CRC.
  • Bernstein, I. H. (1988). Applied Multivariate Analysis. New York: Springer Verlag.
  • Bernstein, I. H. & Teng, G. (1989). Factoring items and factoring scales are different: Spurious evidence for multidimensionality due to item categorization. Psychological Bulletin, 105, 467-477.
  • Bock, R. D., Gibbons, R. & Muraki, E. (1988). Full-information item factor analysis. Applied Psychological Measurement, 12, 261-280.
  • Bolton, R. J., Hand, D. J. & Webb, A. R. (2003). Projection techniques for nonlinear principal component analysis. Statistics and Computing, 13, 267-276.
  • Buja, A. & Eyuboglu, N. (1993). Remarks on parallel analysis. Multivariate Behavioral Research, 27, 509-540.
  • Cañadas, I. y Sánchez-Bruno, A. (1998). Categorías de respuesta en escalas tipo Likert. Psicothema, 10 (3), 623-631.
  • Cid, A. (2004). El clima escolar como factor de calidad en los centros de educación secundaria de la provincia de Ourense. Revista de Investigación Educativa, 22 (1), 113-144.
  • Cliff, N. R. (1988). The eigenvalues-greater-than-one rule and the reliability of components. Psychological Bulletin, 103, 276-279.
  • Cook, D. & Swayne, D. F. (2007). Interactive and dynamic graphics for data analysis with R and Ggobi. New York: Springer.
  • Costello, A. B. & Osborne, J. W. (2005). Best practices in exploratory factor analysis: four recommendations for getting the most from your analysis. Practical Assesment, Research & Evaluation, 10, 1-9.
  • Fernández Díaz, M. J. y Asensio, I. (1993). Evaluación del clima de centros educativos. Revista de Ciencias de la Educación, 153, 69-83.
  • Ferrando, P. J. y Lorenzo, U. (2000). Unrestricted versus restricted factor analysis of multidimensional test item: some aspects of the problem and some suggestions. Psicológica, 21, 301-323.
  • Flora, D. B. & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491.
  • Franklin, S. B., Gibson, D. J., Robertson, P. A., Pohlmann, J. T. & Fralish, J. S. (1995). Parallel Analysis: A Method for Determining Significant Principal Components. Journal of Vegetation Science, 6, 99-106.
  • Gibbons, R. D., Bock, R. D., Hedeker, D., Weiss, D. J., Segawa, E., Bhaumik, D. K., Kupfer, D. J., Frank, E., Grochocinski, V. J. & Stover, A. (2007). Full-information item bifactor analysis of graded responsed data. Applied Psychological Measurement, 31 (1), 4-19.
  • Hair, J. F., Anderson, R. E., Tatham, P. L. & Black, W. C. (1999). Análisis multivariante, Madrid: Prentice Hall.
  • Jöreskog, K. G. (2007). Factor analysis and its extensions. En R. Cudeck & R. C. Maccallum (Eds.), Factor analysis at 100. Historical development and future directions (pp. 47-77). Mahwah, NJ: LEA.
  • Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-27.
  • Kruskal, J. B. (1964b). Nonmetric multidimensional scaling: a numerical method. Psychometrika, 29, 115-129.
  • Little, R. J. A. & Rubin, D. B. (2002). Statistical analysis with missing data. New York: Wiley.
  • Muraki, E. & Carlson, J. E. (1995). Full-information factor analysis for polytomous item responses. Applied Psychological Measurement, 19, 73-90.
  • Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorial, and continuous latent variable indicators. Psychometrika, 49, 115-132.
  • Muthén, B. & Kaplan, D. (1992). A comparison of some methodologies for the factor analysis and non-normal Likert variables: a note on de size of the models. British Journal of the Mathematical and Statistical Psychology, 45, 19-30.
  • Nunnally, J. & Bernstein, I. (1995). Teoría psicométrica. México: McGraw-Hill.
  • 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, Instrumentation, and Computers, 32, 396-402.
  • Pérez-Carbonell, A., Ramos, G. y López-González, E. (en prensa). Diseño y análisis de una escala para la valoración de la variable clima social aula en alumnos de educación primaria y secundaria. Revista de Educación (Madrid).
  • Picón, E., Varela, J. y Real, J. E. (2003). Clasificación y segmentación post hoc mediante el análisis de conglomerados. En J. P. Levy y J. Varela (Eds.), Análisis multivariable para las Ciencias Sociales (pp. 417-450). Madrid: Prentice Hall.
  • Real, J. E. y Varela, J. (2003). Escalamiento multidimensional. En J. P. Levy y J. Varela (Eds.), Análisis multivariable para las Ciencias Sociales (pp. 451-505). Madrid: Prentice Hall.
  • Rivas, T. y Martínez Arias, R. (1991). Relación entre escalamiento multidimensional métrico y análisis de componentes principales. Psicothema, 3, 443-451.
  • Schafer, J. L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.
  • Schriesheim, C. & Castro, S. (1996). Referent effects in the magnitude estimation scaling of frecuency expressions for response anchor sets: an empirical investigation. Educational and Psychological Measurement, 56, 557-569.
  • Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distances function (I y II). Psychometrika, 27, 125-139, 219-246.
  • Shigemasu, K. (1990). Factor analysis of categoriacal data. Recent developments. Japanese Journal of Behaviormetrics, 18, 41-51.
  • Swygert, K. A., Mcleod, L. D. & Thissen, D. (2001). Factor analysis for items or testlets in more than two categories. En D. Thissen & H. Wainer (Eds.), Test Scoring (pp. 217-250). Mahwah, NJ: LEA.
  • Thissen, D. & Wainer, H. (Eds.) (2001) Test Scoring. Mahwah, NJ: LEA.
  • Timm, N.H. (2002). Applied Multivariate Analysis. New York: Springer.
  • Yuan, K. H., Marshall, L. L. & Bentler, P. (2002). A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers. Psychometrika, 67 (1) 95-121.
  • Zwick, W.R. & Velicer, W. F. (1986). Comparison of five rules for determining the Lumber of components to retain. Psychological Bulletin, 99, 432-442.
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