ABSTRACT
As was indicated in Chapter 8, the most important advantage of using IRT is the possibility of applying it in incomplete designs. This does not mean, however, that there are no restrictions on the test designs that can be used in connection with IRT. For this reason, the first section of this chapter is concerned with important features of designs that can be used with IRT models. The next section refers to the problem of parameter estimation. In statistical modelling, the problem of parameter estimation is in many cases technically quite involved, because it amounts generally to solving a complicated set of equations. In this section, technicalities will be skipped almost entirely, because of space limits and, more important, because estimation procedures are usually made available in computer programs that do not require the user to understand all technical considerations. In Section 3, statistical tests are discussed and special attention is given to the problem of power. An IRT model, considered as a complex hypothesis, may be defective in many ways, and some tests are not sensitive to specific defects. It is argued that the most important aspect of testing is the creativity to find ways in which defects may be reflected in some aspects of the data. Careful statistical testing is the key procedure needed to make a considered decision of accepting or rejecting an IRT model and can also be found useful in choosing the most appropriate IRT model and generating relevant person estimates. Finally, in the last section of this chapter, we discuss the problem of how to use the results of an IRT analysis in estimating student achievement and searching for the impact of effectiveness factors operating at different levels.
