Item Response Theory

7Analysis of Dimensionality

It has been stated by economists and by other social scientists that affect cannot be measured, and some of the fundamental theory of social science has been written with this explicit reservation. Our studies have shown that affect can be measured. In extending the methods of psychophysics to the measurement of affect we seem to see the possibility of a wide field of application by which it will be possible to apply the methods of quantitative scientific thinking to the study of feeling and emotion, to esthetics, and to social phenomena.

(Source: L.L. Thurstone)

Much of item response theory (IRT) is based on the assumption of unidimensionality; namely, that the associations among the item responses are explained completely by a single underlying latent variable, representing the target construct being measured. While this is often justified in many areas of educational measurement, more recent interest in measuring patient reported outcomes (Gibbons et al. 2008, 2012) involves items that are drawn from multiple uniquely correlated subdomains violating the usual conditional independence assumption inherent in unidimensional IRT models. As alternatives, both unrestricted item factor analytic models (Bock and Aitkin 1981) and restricted or confirmatory item factor analytic models (Gibbons and Hedeker 1992) have been used to accommodate the multidimensionality of constructs for which the unidimensionality assumption is untenable. A concrete example ...