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## Interdisciplinaria

*versión On-line* ISSN 1668-7027

#### Resumen

RICHAUD, María Cristina. Factor analysis developments to the study of item-level data.* Interdisciplinaria* [online]. 2005, vol.22, n.2, pp.237-251.
ISSN 1668-7027.

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 tetra-choric 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 tetra-choric 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. Another important function of IRT is in the design of appropiateness indices that serve in evaluating validity scales, identifying those protocols that may be characterized by aberrant responding for a set of items. IRT has also been used to develop the full-information item-level factor analysis (Bock, & Schilling, 1997) that direct-ely works on response patterns and avoid the artifacts associated to phi and tetrachoric coefficients (McLeod, Swygert, & Thissen, 2001; Swygert, McLeod, & Thissen, 2001). Summing up, it is necessary to elucidate implications of conceptual models of intelligence and personality assessment and their impact on how one approaches these data statistically (Panter, Swygert, Dahlstrom, & Tanaka, 1997). There are not standar methods nor models that one applies always and in every cases if one really want to obtain valid measures and assessment (Richaud de Minzi, 2005).

**Palabras clave
:
**Dichotomous and ordinal items; Factor analysis; Item Response Theory.