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Although current research suggests that this approach is problematic (Cook, Kallen, and Amtmann, 2009), for the sake of illustration, goodness of ﬁt measures for two conﬁrmatory analyses will be used to compare results of the unidimensional and bifactor conﬁrmatory models. 4 illustrates the two conﬁrmatory factor analysis (n=127,141) using polychoric correlations and robust maximum likelihood estimation yielded from analyses conducted using the EQS statistical package (Bentler, 2006).
To reﬂect the measured attribute, as a single score would not be reﬂective of a speciﬁc trait/ability, for example, depression, anxiety and the like. It is important to note that unidimensionality is never perfect; it is always approximate. The most important question is whether deviation from unidimensionality is substantial enough to warrant the construction of two or more subscales representing distinctions within the measure. Although multidimensional IRT models (MIRT) have been developed (Bartolucci, 2007; Embretson and Yang, 2013; Christensen, Bjorner, Kreiner, and Petersen, 2002; Reckase, 1997; Zwick, 1987) over the past two decades, IRT approaches to multidimensional data are complex, and a detailed explanation is beyond the scope of this chapter.
Although psychotherapy research customarily utilizes summative scores, IRT item-level estimates allow us to determine the contribution of each item to the overall measurement of the latent trait. For example, an item asking about suicidal intent on a depression scale would reﬂect a more substantive contribution to severe depression than would an item indicating feeling blue once in a while, offering a more comprehensive opportunity to investigate and interpret psychotherapy outcomes. One of the most important advantages of the IRT model is the transformation of item responses to a scale-free metric of the latent trait.