| Summary: | This dissertation encompasses three studies on issues of model-data fit methods for latent variable models implemented in modern educational measurement. The first study proposes a new statistic to test the mean-difference of the ability distributions estimated based on the responses of a group of examinees, which can be used to detect aberrant responses of a group of test-takers. The second study is a review of the current model-data fit indexes used for cognitive diagnostic models. Third study introduces a modified version of an existing item fit statistic so that the modified statistic has a known chi-square distribution. Lastly, a discussion of the three studies is given, including the studies’ limitations and thoughts on the direction of future research.
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