ABSTRACT
This chapter aims to discuss the identification problems of binary item response theory models. In 1922, R. A. Fisher pointed out that, in spite of the large amount of fruitful applications of statistics, its basic principles were in a “state of obscurity” and that “during the rapid development of practical methods, fundamental problems have been ignored”. Conceptually speaking, the reduction in data is accomplished by constructing a hypothetical infinite population, of which the actual data are considered a random sample. This hypothetical population is fully characterized by a probability distribution, which in turn is specified by relatively few parameters. This means that each binary Item Response Theory model should be applied to a set of data which, by design, satisfies the identification restrictions.
