Academic journal article The Spanish Journal of Psychology

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

Academic journal article The Spanish Journal of Psychology

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

Article excerpt

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.

Keywords: cut-off scores, standard-setting, multinomial logistic regression, polytomous logistic regression, proportional odds model.

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.

Palabras clave: puntos de corte, establecimiento de estándares, regresión logística multinomial, regresión logística politómica, modelo de odds proporcionales.

(ProQuest: ... denotes formulae omitted.)

In educational and psychological testing, the item responses to a test are usually transformed into a total score that is distributed within a range of values (e.g., from 0 to 50). In some decision making situations, one cut-off score must be established on the total test score in order to classify individuals into two categories (e.g., whether a psychological disorder is present or absent). In clinical settings, this type of problem is frequently solved with the construction of Receiver Operating Characteristic (ROC) curves. ROC analysis was derived from the theory of signal detectability (TSD) which was developed in the early 1950s by engineers working on problems of radar and sonar detection (Peterson, Birdsall & Fox, 1954; Van Meter & Middleton, 1954). ROC curves are used to summarize diagnostic performance of a test by plotting true-positive rate (sensitivity) versus false-positive rate (1- specificity) for each possible cut-off score (threshold). From ROC analysis, a cut-off score on a test can be established taking into account factors such as disorder prevalence (or base rate), and the cost-benefit relation of the various decisions (He, Metz, Tsui, Links & Frey, 2006). …

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