CORRELACIONES POLICÓRICAS Y TETRACÓRICAS EN ESTUDIOS FACTORIALES EXPLORATORIOS Y CONFIRMATORIOS

Agustín Freiberg Hoffmann; Juliana Beatriz Stover; Guadalupe de la Iglesia; Mercedes Fernández Liporace

doi:10.22235/cp.v7i1.1057

Authors

Agustín Freiberg Hoffmann Universidad de Buenos Aires
Juliana Beatriz Stover Universidad de Buenos Aires
Guadalupe de la Iglesia Universidad de Buenos Aires Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
Mercedes Fernández Liporace Universidad de Buenos Aires Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)

DOI:

https://doi.org/10.22235/cp.v7i1.1057

Keywords:

tetrachoric correlations, polychoric correlations, factor analysis, categorical variables, ordinal items, dichotomous items

Abstract

Scientific advances and software development have increased the amount of exploratory and confirmatory studies in psychometric research. Regularly these studies use Pearson´s correlation coefficient, which was originally conceived to be used with continuous variables, and later was extended to categorical items (dichotomous or polytomous). Currently, improved statistical packages allow scientists to carry on robust procedures, designed specifically for categorical variables, among which stand out tetrachoric and polychoric correlations. Since most of psychometric scales consist in dichotomous and polytomous items (mainly Likert formats), the analysis of such correlations becomes methodologically relevant. This paper presents some peculiarities about the use of these statistics, different software packages to facilitate their implementation, as well as the usual problems associated with its employment, and the possible solutions are discussed.

Downloads

Download data is not yet available.

References

Alonso, C.M., Gallego, D.J. y Honey, P. (1994). Los estilos de aprendizaje. Procedimientos de diagnóstico y mejora. Bilbao: Mensajero.

American Psychological Association (2010). Publication manual of the American Psychological Association (6a. ed.) Washington, DC: Author.

Bentler, P.M. (2006). EQS 6 Structural equation program manual. Encino, CA: Multivariate Software, Inc.

Bollen, K.A. (1989). Structural Equations with Latent Variables. New York: Wiley

Boomsma, A. (1983). On the robustness of LISREL (máximum likelihood estimation) against small sample size and non-normality (Tesis Doctoral). Recuperado de http://dissertations.ub.rug.nl/faculties/gmw/1983/a.boomsma/

Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7(3), 461-483.

Brown, T. (2006). Confirmatory Factor Analysis for Applied Research. New York: Guildford Press.

Byrne, B. (2006). Structural Equation Modeling with EQS. New Jersey: Lawrence Erlbaum Associates, Inc., Publishers.

Chen, F., Bollen, K.A., Paxton, P., Curran, P.J., y Kirby, J.B. (2001). Improper solutions in structural equation models. Sociological Methods & Research, 29(4), 468-508.

Choi, J, Peters, M., & Mueller, R. (2010). Correlational analysis of ordinal data: from Pearson´s r to Bayesian polychoric correlation. Asia Pacific Educ.Rev., 11, 459-466. doi: 10.1007/s 12564-010-9096-y

Choi, J., Kim, S., Chen, J., & Dannels, S. (2011). A comparison of máximum likelihood and Bayesina estimation for polychoric correlation using Monte Carlo Simulation. Journal of Educational and Behavioral Statistics, 36(4), 523-549.

Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40(1), 5-32.

Cuttance, P. (2009). Issues and problems in the application of structural equation models. En P. Cuttance & R. Ecob (Eds.), Structural Modeling (pp. 241-280). New York: Cambridge University Press.

Elosua Oliden, P. y Zumbo, B.D. (2008). Coeficientes de fiabilidad para escalas de respuesta categórica ordenada. Psicothema, 20(4), 896-901.

Erceg Hurn, D.M., & Mirosevich, V.M. (2008). Modern robust statistical methods. American Psychologist, 63(7), 591-601.

Ferrando Piera, P.J. y Lorenzo Seva, U. (1993). Algunas relaciones entre el modelo de un factor común y el modelo logístico de dos parámetros. Psicothema, 5(2), 403-412.

Ferrando Piera, P.J., y Lorenzo Seva, U. (1994). Recuperación de la solución factorial a partir de variables dicotomizadas. Psicothema, 6(3), 483-491.

Flora, D., & Curran, P. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466-491.

Forero, C.G., Maydeu Olivares, A., & Gallardo Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling, 16, 625-641.

Freiberg Hoffmann, A. y Fernández Liporace, M.M. (2013). Cuestionario Honey-Alonso de Estilos de Aprendizaje: Análisis de sus propiedades psicométricas en estudiantes universitarios. Revista Summa Psicológica UST, 10(1), 103-117.

Gadermann, A.M., Guhn, M., & Zumbo, D. (2012). Estimating ordinal reliability for likert-tipe and ordinal item response data: a conceptual, empirical, and practical guide. Practical Assessment, Research & Evaluation, 17(3), 1-13.

Gerbing, D.W. & Anderson, J.C. (1987). Improper solutions in the analysis of covariance structures: their interpretability and a comparison of alternate respecifications. Psychometrika, 52(1), 99-111.

González Álvarez, N., Abad González, J. y Leví Mangin, J.P. (2006). Normalidad y otros supuestos en análisis de covarianzas. En J.P. Lévy Mangin y J. Varela (Eds.), Modelización con estructuras de covacianzas en ciencias sociales (pp. 31-59). Coruña: Netbiblo.

Hair, J.F., Anderson, R.E, Tatham, R.L. y Black, W.C. (1999). Análisis multivariante. Madrid: Prentice Hall.

Holgado Tello, F., 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.

Hoyle, R.H. (1995). Structural Equation Modeling. California: SAGE Publications, Inc.

IBM Corporation (2012a). IBM SPSS Statistics (21). Recuperado de http://www-01.ibm.com/software/es/analytics/spss/

IBM Corporation (2012b). IBM SPSS Amos (21). Recuperado de http://www-01.ibm.com/support/docview.wss?uid=swg27035758

Jöreskog, K.G. (2001). Analysis of ordinal variables 2. Cross-sectional data. Taller “Structural Equation Modelling with LISREL 8.51”. Friedrich-Schiller-Universitat, Jena.

Jöreskog, K.G., & Sörbom, D. (1999). LISREL 8: user´s reference guide. Lincolnwood, IL: Scientific Software International, Inc.

Juras, J., & Pasaric, Z. (2006). Aplication of tetrachoric and polychoric correlation coefficients to forecast verification. GEOFIZIKA, 23(1), 59-82.

Katsikatsou, M., Moustaki, I., Yang-Wallentin, F., & Jöreskog, K. (2012). Pair wise likelihood estimation for factor analysis models with ordinal data. Computational Statistics and Data Analysis, 56(12), 4243-4258.

Kelloway, E.K. (1998). Using LISREL for structural equation modeling. Thousand Oaks: Sage Publications.

Kline, P. (2000). Handbook of Psychological Testing (2a. ed.). New York: Routledge.

Kline, R. B. (2005). Structural equation modeling. New York: Guilford Press.

Kolenikov, S., Bollen, K.A., & Savalei, V. (2006). Specification test with Heywood cases. Recuperado de http://web.missouri.edu/~kolenikovs/ASA06procrefs.pdf

Lévy Mangin, J.P. y González, N. (2006). Modelización y Causalidad. En J.P. Lévy Mangin y J. Varela Mallou (Eds.), Modelización con estructuras de covacianzas en ciencias sociales (pp. 155-175). Coruña: Netbiblo.

Lévy Mangin, J.P., Martín Fuentes, M.T. y Román González, M.V. (2006). Optimización según estructuras de covarianzas. En J.P. Lévy Mangin y J. Varela (Eds.), Modelización con estructuras de covacianzas en ciencias sociales (pp. 11-30). Coruña: Netbiblo.

Lorenzo Seva, U., & Ferrando Piera, P.J. (2012). Manual of the Program FACTOR. Recuperado de http://psico.fcep.urv.es/utilitats/factor/

Manzano Patiño, A. y Zamora Muñoz, S. (2009). Sistema de ecuaciones estructurales: una herramienta de investigación. Cuaderno técnico 4. Recuperado de http://www.senasica.gob.mx/includes/asp/download.asp?iddocumento=23068&idurl=45367

Martínez Arias, R. (2005). Psicometría: teoría de los tests psicológicos y educativos. Madrid: Síntesis.

Maydeu Olivares, A, Forero, C.G., Gallardo Pujol, D., & Renom, J. (2009). Testing categorized bivariate normality with two-stage polychoric correlations estimates. Europeal Joournal of Research Methods for the Behavioral and Social Sciences, 5, 131-136.

Méndez Alonso, A. (2001). Estimación robusta: Una aplicación informática con fines didácticos. Estadística Española, 43(147), 105-123.

Moos, R.H. (1993). Coping Responses Inventory – Youth Form. Odessa: Psychological Assessment Resources.

Morales Vallejo, P. (2006). Medición de actitudes en Psicología y Educación. Madrid: Universidad Pontificia Comillas.

Multivariate Software (2012). EQS (6.2). Recuperado de http://www.mvsoft.com/eqsdownload.htm

Muthén, B. (1983). Latent variable structural equation modeling with categorical data. Journal of Econometrics, 22, 43-65.

Muthén, B. (1984). A general estructural equation model with dichotomous ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115-132.

Muthén, B. (1989). Dichotomous factor analysis of symptom data. En Eaton, y Bohrnstedt (Eds.), Latent Variable Models for Dichotomous Outcomes: Analysis of Data from the Epidemiological Catchment Area Program (pp. 19-65), Sociological Methods & Research, 18, 19-65.

Muthén, B., & Hofacker, C. (1988).Testing the assumptions underlying tetrachoric correlations. Psychometrika, 53(4), 563-578.

Muthén, B., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171-189.

Muthén, L., & Muthén, B. (2012). MPLUS (7). Recuperado de http://www.statmodel.com/index.shtml

Nunnally, J.C., y Bernstein, I.H. (1994). Psychometric Theory (3a ed.). New York: McGraw-Hill.

Ogasawara, H. (2011). Asymptotic expansions of the distributions of the polyserial correlations coefficients. Behaviormetrika, 38(2), 153-168.

Olsson, U.H., Foss, T., Troye, S.V., & Howell, R.D. (2000). The performance of ML, GLS and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling, 7(4), 557-595.

Ortiz León, M.C. (1988). Inferencia estadística robusta. Revista la Ciencia y el Hombre, 2, 95-106.

Pfanzagl, J. (1968). Theory of measurement. New York: John Wiley.

Rial Boubeta, A., de la Iglesia, G., Ongarato, P. y Fernández Liporace, M. (2011). Dimensionalidad del Inventario de Afrontamiento para adolescentes y universitarios. Psicothema, 23(3), 464-474.

Rial Boubeta, A., Varela Mallou, J., Abalo Piñeiro, J. y Lévy Mangin, J.P. (2006). El análisis factorial confirmatorio. En: J.P. Lévy Mangin y J. Varela (Eds.), Modelización con estructuras de covarianzas en ciencias sociales (pp. 119-143). Coruña: Netbiblo.

Richaud, M.C. (2005). Desarrollos del análisis factorial para el estudio de ítem dicotómicos y ordinales. Revista Interdisciplinaria, 22(2), 237-251.

Saris, W.E., Scherpenzeel, A.C., & Wijk, T. (1998). Validity and reliability of subjective social indicators: the effect of different measures of association. Social Indicators Research, 45, 173-199.

Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Test of significance and descriptive goodness-of-fit measures. Methods of Psychological Research Online, 8(2), 23-74.

Schumacker, R.E., & Lomax, R.G. (2004). A beginner´s guide to estructural equation modeling (2a ed.). New Jersey, London: Lawrence Erlbaum Associates.

Scientific Software International (2006). LISREL (8). Recuperado de http://www.ssicentral.com/lisrel/resources.html

Stevens, S.S. (1951). Mathematics, measurement and psychophysics. En S.S. Stevens (Ed.), Handbook of Experimental Psychology (pp. 1-30). New York: Wiley.

SYSTAT Software (2010). SYSTAT (13.1). Recuperado de http://www.systat.com/SystatProducts.aspx

Torgerson, W.S. (1958). Theory and methods of scaling. New York: John Wiley.

West, S.G., Finch, J.F., & Curran, P.J. (1995).Structural equation models with nonnormal variables: problems and remedies. En: R.H. Hoyle (Ed.), Structural Equation Modeling (pp. 56-76). California: SAGE Publications, Inc.

Yela, M. (1966). Los tests y el análisis factorial. En B. Szekeli (Ed.), Los Tests (pp. 153-178). Buenos Aires: Kapelusz.

Yung, Y.F., & Bentler, P.M. (1994). Bootstrap-corrected ADF test statistics in covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 47, 63-84.