Interpretation of the three-parameter testlet response model and information function

The testlet response model is designed for handling items that are clustered, such as those embedded within the same reading passage. Although the testlet is a powerful tool for handling item clusters in educational and psychological testing, the interpretations of its item parameters, the conditional correlation between item pairs, and the testlet information function are not always clear. For example, the a-parameter in a testlet response model, which is sometimes referred to as the discrimination parameter and interpreted in the conventional way, is often directly compared to the a-parameter in standard item response models. In this article, it is argued that despite the deceptively similar forms of the a-parameters, such interpretation and comparison can be misleading. A marginalized version of the testlet model is introduced to derive quantities that are comparable to standard item response models. This mean (marginal-ization) of the function approach is contrasted with the temptingly simple but inappropriate func-tion of the mean approach, in which the testlet effect is set to its mean of zero in respective equations for item response, correlation, and information functions. Testlet data collected from a science assessment within the National Assessment of Educational Progress are used to illustrate the subtle differences in the interpretations of the various response models