Item Response Models for Dependent Data: Quasi-exact Tests for the Investigation of Some Preconditions for Measuring Change

The Rasch model has several advantages for the psychometric investigation of item quality (e.g., specific objectivity). One approach to testing model fit uses quasi-exact tests which are well suited to test the validity of the Rasch model when sample sizes are rather small. Application of these tests is not restricted to Rasch modeling. In this chapter, we show that these tests can be used to test preconditions for measuring change such as measurement invariance, unidimensionality, and local independence across time points. For example, if items are unidimensional across time points (i.e., all items measure the same latent construct across time) and groups (e.g., control and training groups), it follows that there are no significant interindividual differences within groups and over time. All individuals in a group change in the same direction. On the other hand, significant results across time but not within groups suggest group differences in change, such as training effects. In this chapter, we first give an introduction to quasi-exact tests. Then, we demonstrate the applicability of three test statistics for the investigation of preconditions for measuring change using empirical power analysis and an empirical example concerning spatial ability.