Desarrollos del análisis factorial para el estudio de ítems dicotómicos y ordinales

Abstract

Los ítem de evaluación cualitativa (dicotómicos u ordinales) presentan problemas específicos para la utilización del análisis factorial en las pruebas de personalidad. En el presente trabajo se revisan algunos desarrollos recientes en análisis factorial que resultan apropiados para este tipo de ítem. Estos desarrollos se han realizado en el contexto de dos modelos estadísticos: la Teoría de la Respuesta al Item y el modelo de las ecuaciones estructurales. También se verá la relevancia del escalamiento de ítem en el contexto de estos dos modelos. Se presentan algunos ejemplos de la utilidad de estos modelos para resolver cuestiones básicas, tales como la dimensionalidad de la escala y las propiedades generales de los ítem, la adecuación de las respuestas observadas y el funcionamiento diferencial del ítem a través de diferentes submuestras.

Factor analysis has been used in formulating conceptual models in personality and personality assessment, as well as in the process of construction of personality scales. Factor analysis assumes continuously measured interval level data. However, applications of the factor analysis model in the personality literature frequently are conducted using dichotomous or ordinal data obtained at the item level. It has been proposed several solutions for studying dichotomous or ordinal data. Christoffersson (1978) introduced a method for factor analyzing dichotomous data using tetrachoric correlations. Muthén (1984) extended this method to provide a less computationally heavy approach. Standard factor analysis implies two different levels of variables: unobserved factors, and observed indicators for those factors (items). The generalized least squares method to the factor analysis of dichotomous data requires one additional intermediate level between the observed data and the latent variable. Thus two levels of abstraction are involved in the analysis: observed dichotomous or ordered categorical items are linked to unobserved latent response variables via tetrachoric or polychoric correlations. These unobserved latent response variables then serve as the indicators for the factors. In this model the factors summarize the relations among latent variables rather than directly among observed variables. Another method for the factor analysis of dichotomous or ordered categorical items is that of maximum likelihood. As in the case of the generalized least squares method, the maximum likelihood approach use tetrachoric correlations among items, but approximates a numerical integration of a distribution of observations, assumed to be normal, using weighted sums. There exist also parallel analysis programs (Buja, & Eyuboglu, 1992; Horn, 1965) that produce data sets based in aleatory numbers normally distributed, generated by the computer (O'Connor, 2000). Another manner of analysis of relationships between unobserved factors and observed dichotomous or ordinal data is that of aplying Item Response Theory (IRT). In conjunction with exploratory item-level factor analises that adress the underlying dimensionality of the item set, IRT and confirmatory item-level factor analyses are useful for the construction and validation of personality inventories.