Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling "construct-relevant" multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957) and highlight its…

Twelve articles (including two rounds of commentary) consider the proposition that the use of multi-item scales requires only that conditions of simple structure and metric invariance be satisfied at the scale level, rather than for each item individually. The place of the approach in confirmatory factor analysis is debated. (SLD)

The factor analysis of ordered-categorical measures has been described in the literature on factor analysis, but the extension of the analysis to the multiple-population case is less well-known. For example, a comprehensive statement of identification conditions for the multiplepopulation case seems absent in the literature. We review this…