## Item Response Theory as Ideal Model

During the 1950s and 1960s, a revolutionary test theory, now known as IRT, was developed (Birnbaum, 1968; Lord, 1952; Lord and Novick, 1968; Rasch, 1960). IRT had the desirable features of an alternative test theory that were described above. That is, unlike CTT, the examinee's true score is not test dependent, the item parameters are not sample dependent, and the parallel test assumption is not necessary in IRT. In other words, if a given IRT model fits the test data of interest, ability estimates obtained from different sets of items will be comparable. Furthermore, item parameter estimates are also comparable regardless of the groups of examinees (Hambleton et al, 1991).

IRT also includes indices to discern the strength and weakness of each item in a test. In contrast, the CTT analyses are focused on the scale at the test level. For example, in IRT, we can distinguish good and bad items in terms of how accurately an item can measure examinees' at the different trait levels (i.e., item information). Also, IRT has provided solutions for many practical testing problems such as equating different test forms and examining measurement bias (Embretson and Reise, 2000).

There are two basic assumptions of IRT models about the data to which the models are applied: appropriate dimensionality and local independence. The first assumption means that the number of latent traits measured by the items corresponds to the number of trait parameters in the IRT model. For example, if test items depend on two or more latent traits, then IRT models with a single person trait parameter will not be appropriate. Factor analysis, among other methods, can be used to test the assumption. Models which assume the measurement of more than one trait for examinees' test scores are referred to as multidimensional models (Hambleton et al, 1991). Several multidimensional IRT (MIRT) models allow for more than one trait (0) to be estimated, even though the most widely applied IRT models assume a unidimensional construct for which one 0 estimate is sufficient to explain item responses (Reckase, 1997).

The unidimensionality assumption is closely related to the assumption of local independence. The local independence assumption means that when the abilities to influence test scores are controlled, examinees' responses to any of the items are statistically independent. Alternatively, within a given trait level, the probability of getting one item correct is independent of the probability of getting other items correct.

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