LATENT TRAIT MODELS AND THEIR USE IN THE ANALYSIS OF EDUCATIONAL TEST DATA1,2,3

A theory of latent traits supposes that in testing situations, examinee performance on a test can be predicted (or explained) by defining characteristics of examinees, referred to as traits, estimating scores for examinees on these traits, and using the scores to predict or explain test performance (Lord and Novick, 1968). Since the traits are not directly measurable and therefore "unobservable," they are often referred to as latent traits or abilities. A latent trait model specifies a relationship between observable examinee test performance and the unobservable traits or abilities assumed to underlie performance on the test. The relationship between the "observable" and the "unobservable" quantities is described by a mathematical function. For this reason, latent trait models are mathematical models. Also, latent trait models are based on assumptions about the test data. When selecting a particular latent trait model to apply to one's test data, it is necessary to consider whether the test data satisfy the assumptions of the model. If they do not, different test models should be considered. Alternately, some psychometricians (for example, Wright, 1968) have recommended that test developers design their tests so as to satisfy the assumptions of the particular latent trait model they are interested in using. Recent work by Lord (1968, 1974a), Lord and Novick (1968), Wright (1968), Wright and Panchapakesan (1969), Samejima (1969, 1972), Bock and Wood (1971), and Whitely and Dawis (1974) has been helpful in introducing educational measurement specialists to the topic of latent trait models. Also, the work of these and other individuals has contributed substantially to the current interest among test practitioners in applying the models to a wide variety of educational and psychological testing problems. Latent trait models are now being used to "explain" examinee test performance as well as to provide a framework for solving test design problems and other important testing questions that have, to date, gone unresolved (Lord, 1977; Wright, 1977a, 1977b). Why has the use of latent trait models in practical testing situations been low? There are at least five reasons. For one, the topic of latent trait theory represents a complex branch of the field of test theory. The advanced mathematical skills required to study many of the papers published on the topic have probably discouraged many potential

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