Behavioral and social scientists are acutely aware that most phenomena of interest to them are only indirectly observable. Concepts such as intelligence, motivation, achievement, language proficiency, self-efficacy, happiness, depression, and so forth are abstractions that serve the purpose of reducing to a single label what is an otherwise complex constellation of observable behaviors. In the vernacular of

the social and behavioral sciences, this distinction between that which is directly observable and that which must be inferred on the basis of covariation among those observables is known as the distinction between manifest (observable) and latent (unobservable) variables. The introduction of latent variables into psychological measurement dates to the start of the last century through the work of Spearman on intelligence (Spearman, 1904, as cited in Borsboom, Mellenbergh, & van Heerden, 2003). To be clear, latent variables are not latent in the individual, but latent in the direct observations that scientists make on their subjects. Borsboom et al. (2003) distinguish two ways in which latent variables are used: The first is a formal, technical way, which at its roots is a mathematical formulation that describes the relations among directly observable variables in terms of their relations with the underlying latent variables. The second is empirical and reflects the combining of scores on observable variables into estimates of scores on the underlying latent variables. Although these two uses are inextricably connected, they are distinguishable from one another, and it is generally in the former sense that the term latent variable is used throughout this chapter.