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A General Equation to Obtain Multiple Cut-off Scores on a Test from Multinomial Logistic Regression

Published online by Cambridge University Press:  10 January 2013

Rosa Bersabé  and
Teresa Rivas
Rosa Bersabé*
Affiliation:
Universidad de Málaga (Spain)
Teresa Rivas
Affiliation:
Universidad de Málaga (Spain)
*
Correspondence concerning this article should be adressed to Rosa Bersabé Morán. Departamento de Psicobiología y Metodología de las Ciencias del Comportamiento. Facultad de Psicología. Universidad de Málaga. 29071 Málaga. (Spain). E-mail: [email protected]
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Abstract

The authors derive a general equation to compute multiple cut-offs on a total test score in order to classify individuals into more than two ordinal categories. The equation is derived from the multinomial logistic regression (MLR) model, which is an extension of the binary logistic regression (BLR) model to accommodate polytomous outcome variables. From this analytical procedure, cut-off scores are established at the test score (the predictor variable) at which an individual is as likely to be in category j as in category j+1 of an ordinal outcome variable. The application of the complete procedure is illustrated by an example with data from an actual study on eating disorders. In this example, two cut-off scores on the Eating Attitudes Test (EAT-26) scores are obtained in order to classify individuals into three ordinal categories: asymptomatic, symptomatic and eating disorder. Diagnoses were made from the responses to a self-report (Q-EDD) that operationalises DSM-IV criteria for eating disorders. Alternatives to the MLR model to set multiple cut-off scores are discussed.

En este artículo, las autoras derivan una ecuación general para calcular múltiples puntos de corte en la puntuación total de un test con el fin de clasificar a los individuos en más de dos categorías ordinales. La ecuación se deriva a partir del modelo de regresión logística multinomial (RLM), que es una extensión del modelo de regresión logística binaria (BLR) para variables de respuesta politómica. Con este procedimiento analítico, los puntos de corte se establecen en la puntuación del test (la variable predictora) en la que un individuo tiene la misma probabilidad de pertenecer a la categoría j que a la categoría j+1 de una variable de respuesta ordinal. La aplicación del procedimiento completo se ilustra a través de un ejemplo con datos de un estudio real sobre trastornos de la conducta alimentaria. En este ejemplo se obtienen dos puntos de corte en las puntuaciones del Test de Actitudes Alimentarias (EAT-26) para clasificar a los individuos en tres categorías ordinales: asintomático, sintomático o con trastorno de la conducta alimentaria. Los diagnósticos se obtuvieron a partir de las respuestas a un autoinforme (Q-EDD) en el que se operativizan los criterios del DSM-IV para los trastornos de la conducta alimentaria. Se discuten diferentes alternativas al modelo RLM para establecer múltiples puntos de corte.

Keywords

cut-off scoresstandard-settingmultinomial logistic regressionpolytomous logistic regressionproportional odds modelpuntos de corteestablecimiento de estándaresregresión logística multinomialregresión logística politómicamodelo de odds proporcionales
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 13 , Issue 1 , May 2010 , pp. 494 - 502
Copyright
Copyright © Cambridge University Press 2010

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References

Agresti, A. (2002). Categorical Data Analysis, 2nd ed. New York: John Wiley & Sons.CrossRefGoogle Scholar
Allison, P. D. (1999). Logistic Regression Using the SAS System: Theory and Application. Cary, NC: SAS Institute Inc.Google Scholar
American Psychiatric Association (1994). Diagnostic and statistical manual of mental disorders (4th ed.). Washington, DC: Author.Google Scholar
Ananth, C. V., & Kleinbaum, D. G. (1997). Regression models for ordinal responses: A review of methods and applications. International Journal of Epidemiology, 26, 1323–1333.CrossRefGoogle ScholarPubMed
Bender, R., & Grouven, U. (1998). Using binary logistic regression models for ordinal data with non-proportional odds. Journal of Clinical Epidemiology, 51, 809–816.CrossRefGoogle ScholarPubMed
Bersabé, R., Rivas, T., & Berrocal, C. (2009). Obtaining equations from the proportional odds model to set multiple cut scores on a test. Methodology, 5, 123–130.CrossRefGoogle Scholar
Castro, J., Toro, J., Salamero, M., & Guimera, E. (1991). The Eating Attitudes Test: Validation of the Spanish version. Psychological Evaluation, 7(2), 175–189.Google Scholar
Cizek, G. J., & Bunch, M., B. (2007). Standard setting. A guide to establishing and evaluating performance standards on tests. Thousand Oaks, CA: Sage.Google Scholar
Cizek, G. J., Bunch, M.B., & Koons, H. (2004). Setting performance standards: Contemporary methods. Educational Measurement: Issues and Practice, 23, 31–50.CrossRefGoogle Scholar
Garner, D.M., & Garfinkel, P.E. (1979). The Eating Attitudes Test: An index of the symptoms of anorexia nervosa. Psychological Medicine, 9, 273–279.CrossRefGoogle ScholarPubMed
Garner, D.M., Olmsted, M.P., Bohr, Y., & Garfinkel, P.E. (1982). The Eating Attitudes Test: psychometric features and clinical correlates. Psychological Medicine, 12, 871–878.CrossRefGoogle ScholarPubMed
He, X., Metz, C. E., Tsui, B. M. W., Links, J. M., & Frey, E. C. (2006). Three-Class ROC Analysis-A Decision Theoretic Approach Under the Ideal Observer Framework. IEEE Transactions on Medical Imaging, 25, 571–581.Google ScholarPubMed
Hosmer, D. W., & Lemeshow, S. (2000). Applied Logistic Regression, 2nd ed. New York: Wiley.CrossRefGoogle Scholar
Kingston, N. M., Kahl, S. R., Sweeney, K., & Bay, L. (2001). Setting performance standards using the body of work method. In Cizek, G. J. (Ed.), Setting performance standards: Concepts, methods, and perspectives (pp. 219–248). Mahwah, NJ: Erlbaum.Google Scholar
Kleinbaum, D. G., & Klein, M. (2002). Logistic Regresión. A Self-Learning Text, 2nd ed. London: Springer.Google Scholar
Long, J. S. (1997). Regression models for categorical and limited dependent variables. Thousand Oaks, CA: Sage.Google Scholar
McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society, Series B, 42, 109–142.Google Scholar
Menard, S. (1995). Applied logistic regression analysis. Thousand Oaks, CA: Sage.Google Scholar
Menard, S. (2000). Coefficients of determination for multiple logistic regression analysis. The American Statistician, 54, 17–24.Google Scholar
Mintz, L. B., O'Halloran, M. S., Mulholland, A. M., & Schneider, P. A. (1997). Questionnaire for Eating Disorder Diagnoses: Reliability and validity of operationalizing DSM-IV criteria into a self-report format. Journal of Counseling Psychology, 44, 63–79.CrossRefGoogle Scholar
Mossman, D. (1999). Three-way ROCs. Medical Decision Making, 19, 78–89.CrossRefGoogle ScholarPubMed
O'Connell, A. A. (2006). Logistic regression models for ordinal response variables. Thousand Oaks, CA: Sage.CrossRefGoogle Scholar
Peterson, W. W., Birdsall, T. G., & Fox, W. C. (1954). The theory of signal detectability. Transactions of the IRE Professional Group of Information Theory, 4, 171–212.CrossRefGoogle Scholar
Plake, B. S., & Hambleton, R. K. (2001). The analytic judgment method for setting standards on complex performance assessments. In Cizek, G. J. (Ed.), Setting performance standards: Concepts, methods, and perspectives (pp. 283–312). Mahwah, NJ: Erlbaum.Google Scholar
Provost, F., & Fawcett, T. (2001). Robust Classification for Imprecise Environments. Machine Learning, 42, 203–231.CrossRefGoogle Scholar
R Development Core Team (2008). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing. Retrieved April 18, 2008, from: http://www.R-project.org/.Google Scholar
Revelle, W. (2007). Using R for psychological research: A simple guide to an elegant package. Retrieved June 21, 2008, from: http://www.personality-project.org/r/r.guideGoogle Scholar
Rivas, T., Bersabé, R., & Castro, S. (2001). Propiedades psicométricas del Cuestionario para el Diagnóstico de los Trastornos de la Conducta Alimentaria (Q-EDD). Psicología Conductual, 9, 255–266.Google Scholar
Rivas, T., Bersabé, R., Jiménez, M., & Berrocal, C. (in press). The Eating Attitudes Test (EAT-26): Reliability and Validity in Spanish Female Samples. The Spanish Journal of Psychology.Google Scholar
SAS Institute, Inc (2000). SAS/STAT User's Guide, Version 8.0. Cary, NC: Author.Google Scholar
Scurfield, B. K. (1996). Multiple-event forced-choice tasks in the theory of signal detectability. Journal of Mathematical Psychology, 40, 253–269.CrossRefGoogle ScholarPubMed
Scurfield, B. K. (1998). Generalization of the theory of signal detectability to n-event m-dimensional forced-choice tasks. Journal of Mathematical Psychology, 42, 5–31.CrossRefGoogle ScholarPubMed
SPSS, Inc (2006). SPSS 14.0 Base User's Guide. Chicago, IL: Author.Google Scholar
Stokes, M. E., Davis, C. S., & Koch, G. G. (2000). Categorical Data Analysis Using the SAS System, Second Edition. Cary, NC: SAS Institute Inc.Google Scholar
Van Meter, D., & Middleton, D. (1954). Modern statistical approaches to reception in communication theory. Transactions of the IRE Professional Group of Information Theory, 4, 119–145.CrossRefGoogle Scholar
Venables, W. N., & Ripley, B. D. (2002). Modern Applied Statistics with S, 4th ed. New York: Springer. Retrieved May 5, 2008, from: http://www.stats.ox.ac.uk/pub/MASS4.CrossRefGoogle Scholar
Venables, W. N., Smith, D. M., & R Development Core (2004). An Introduction to R. Network Theory Limited. Retrieved June 7, 2008, from: http://cran.r-project.org/manuals.htmlGoogle Scholar