ABSTRACT
Multidimensional item response theory (MIRT) is not a theory in the usual scientific sense of the use of the word, but rather, it is a general class of theories. These theories are about the relationship between the probability of a response to a task on a test and the location of an examinee in a construct space that represents the skills and knowledge that are the targets of measurement for the test. The tasks on the test are usually called test items. Included in the development of the general class of theories are implicit assumptions that people vary in many ways related to the constructs that are the target of the test, and the test items are sensitive to differences on multiple constructs. An important aspect of MIRT is that certain mathematical functions can be used to approximate the relationship between the probabilities of the scores on a test item and the locations of individuals in the construct space (Albert, Volume Two, Chapter 1). This chapter focuses on special cases of MIRT models that are based on one common form for the mathematical function, the cumulative logistic function. This particular functional form is used to relate the probability of the item score for a test item to the location of an individual in the latent space. If this function is found to fit well a matrix of item responses obtained from administering a test to a group of individuals, then there are a number of useful results that can be obtained from the use of this function as a mathematical model. This chapter describes several forms of the MIRT models based on the cumulative logistic function and shows how they can be used to provide useful information about the locations of examinees in the multidimensional latent space.
