Estimation of Item and Person Parameters
The MIRT models presented in this book are useful from a theoretical perspective because they provide a model for the interaction between persons and test items. The different kinds of models represent different theoretical perspectives. For example, the compensatory and partially compensatory models provide two different conceptions of how levels on hypothetical constructs combine when applied to items that require some level on the constructs to determine the correct response. Although the theoretical models are interesting in their own right, the practical applications of the models require a means of estimating the item and person parameters for the models. Without practical procedures for parameter estimation, the usefulness of the models is very limited.
This chapter describes the procedures that are currently used for estimating the item and person parameters for the models. These procedures are necessarily embedded within computer programs for carrying out the steps in the estimation methodology. It is difficult to separate the estimation procedures from the programs used to implement them. An excellent estimation methodology may perform poorly because it is improperly programmed or programmed in an inefficient way. A method with poorer theoretical properties may perform better overall because the programming of the method was done in a more creative way. Because of this close tie between estimation methodology and the computer programs used to implement them, they will be described together in the later sections of this chapter. Before getting into the details of estimation procedures, a general overview is provided. This overview is designed to give a conceptual framework for understanding the estimation procedures without getting into the technical details.
This chapter is reasonably up to date about programs and methods as of 2008. However, computer software becomes obsolete and computer systems change fairly rapidly. For that reason, this chapter does not go into the details of running specific programs. Those may change by the time this book is published. Rather, the basic estimation model is described for commonly used programs and differences in constraints used in estimation procedures are presented. These are the features of the estimation methods and programs that explain why different programs applied to the same item response data give different parameter estimates. Chapter 7 describes some methods for determining if the parameter estimates from different programs are simple transformations of each other.
KeywordsMarkov Chain Monte Carlo Test Item Item Score Item Parameter Quadrature Point
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