Statistical models that incorporate latent variables (i.e., variables that are inherently unobservable) began at least as early as the observation of Spearman (1904) that scores on different educational or academic tests were usually positively correlated; that is, examinees performing well on one academic test often performed well on other tests. This phenomenon was observed in many circumstances, and Spearman concluded that it could be explained by a simple statistical model in which each examinee was postulated as having an underlying unidimensional, but not directly observed, “academic ability” or “general intelligence” that varied from person to person. He assumed that this ability was positively related to a person’s performance on each of the different tests. The higher a person’s ability, the higher he or she tended to score on any test of some aspect of academic or intellectual performance.
Spearman’s simple model was elaborated and led to the development of factor analysis as a statistical methodology, as well as to various theories of intelligence, as a topic within psychology. Early references to factor analysis are Spearman (1904), Thurstone (1931), and Kelley (1935).
Closely related to factor analysis was true score theory, in which a single educational or “mental” test was the object of study rather than several tests. In this framework, observed test scores were considered the result of a latent true score plus measurement error. This was a powerful theory that allowed the development of quantitative measures of reliability and validity that have become routine measures of the efficacy of any test (Spearman, 1907; Kelly, 1923).
Starting in the 1940s, latent structure or latent class models were developed and applied to sets of individual test or survey questions to produce scales for both the questions and the respondents (Stouffer et al., 1950). These were further developed in Anderson (1954) and Lazarsfeld and Henry (1968). At roughly the same time, item response theory, of which the Rasch model is an example, was developed for educational and psychological tests (Lawley, 1943; Tucker, 1946; Lord, 1952; Rasch, 1960; Birnbaum, 1968; Lord, 1980). The word “item” in item response theory is a term used by test developers and psychometricians to refer to the questions on tests and the rules for scoring them.
Bartholomew (1987) gives a unified discussion of the three related types of latent variable models—factor analysis, latent class analysis, and item response theory. This general class of statistical models is discussed more extensively next.