ABSTRACT
Lazarsfeld began the development of a group of models under the title latent structure analysis. Because terminology in this area has not yet stabilized, this chapter reviews the collection of models for binary as constituting latent trait theory or, interchangeably, item response theory. The object of the chapter is to make a brief examination of some of the key concepts of classical test theory from a factor-analytic perspective. From a factor-analytic point of view the Rasch model is a nonlinear transformation of the special case of the Spearman single-factor model in which the factor loadings are required to be all the same. One of the central objects of classical test theory was to obtain an estimate of the error variance of a test, typically from the product of the reliability coefficient of the test, defined as the ratio of its true-score variance to its total variance and the total variance of the test score, however it happens to be scaled.
