A basic IRT model assumes a one-dimensional latent variable representing the trait that predicts the probability of a certain response on a particular item: the higher the latent trait value, the higher the probability of a high score on the item. Item parameters determine the exact relationship between the latent trait and the probability of the response to a particular item. The so-called difficulty parameter provides information about the general probability of a positive response to a particular item, and is very similar to the threshold parameter in liability models. The discrimination parameter value of an item indicates how strong the relationship is between the latent trait and the item response variable, and is therefore similar to a factor loading. Because latent scores are estimated conditional on the item parameters for the administered items, the scoring process becomes independent of the particular items in the test. For example, this allows the comparison of a child’s achievement on a test with easy questions with the achievement of another child on a test with difficult questions. IRT test linking was applied in
