The Challenges of Fitting an Item Response Theory Model to the Social Anhedonia Scale

Abstract

This study explored the application of latent variable measurement models to the Social Anhedonia Scale (SAS; Eckblad, Chapman, Chapman, & Mishlove, 1982), a widely used and influential measure in schizophrenia-related research. Specifically, we applied unidimensional and bifactor item response theory (IRT) models to data from a community sample of young adults (n = 2,227). Ordinal factor analyses revealed that identifying a coherent latent structure in the 40-item SAS data was challenging due to (a) the presence of multiple small content clusters (e.g., doublets); (b) modest relations between those clusters, which, in turn, implies a general factor of only modest strength; (c) items that shared little variance with the majority of items; and (d) cross-loadings in bifactor solutions. Consequently, we conclude that SAS responses cannot be modeled accurately by either unidimensional or bifactor IRT models. Although the application of a bifactor model to a reduced 17-item set met with better success, significant psychometric and substantive problems remained. Results highlight the challenges of applying latent variable models to scales that were not originally designed to fit these models.

Acknowledgments

This work was supported by the National Institute of Mental Health (Blanchard: R01MH51240, K02MH079231, R01MH082839; Horan: R01MH82782).

Notes

A model with two or more correlated factors is also a well-known and plausible latent structure for the SAS. This model proposes that subsets of items are indicative of distinct separate dimensions, and in turn, these dimensions are correlated. However, this correlated-traits model does not directly model a common latent variable of social anhedonia that runs among the items. Instead, such a model needs to be extended to represent social anhedonia as a second-order factor that explains the correlation among primary traits. Because second-order models, which are nested under confirmatory bifactor models, do not directly model the relation between items and a second-order dimension, they are not considered further in this article.

First, note that this is a “compensatory” model—high levels on either the general or group latent trait increase the probability of endorsing the item. Second, the γ _i in Equation 2 is simply a multidimensional intercept parameter. Unlike the location parameter in unidimensional IRT models, the multidimensional intercept has no simple interpretation.

This model was identified by specifying that each of the primary dimensions is equally related to a higher order dimension.

Models up to seven group factors were also investigated, but these solutions tended to have group factors that were not well defined (e.g., only one or two items loading highly on a factor).