A modified higher-order DINA model for detecting differential item functioning and differential attribute functioning
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This dissertation presents a modified higher-order DINA model for separating the source of construct-relevant (i.e., benign) differential item functioning (DIF) from construct irrelevant (i.e., adverse) DIF. The model-based method provides a natural framework for detecting both differential attribute functioning (DAF) and DIF in a cognitive diagnostic modeling framework: DIF detection ensures test fairness and improves test validity in terms of group difference in item performance after conditioning on attribute mastery profiles, whereas DAF detection provides a good understanding of group strength and weakness in terms of a set of cognitive attributes after conditioning on general ability. An MCMC algorithm employing Gibbs sampling was used to estimate the new model and a simulation study was done to examine model recovery, Type I error rates, and power under different testing conditions. For DIF detection, the model-based method was also compared with the MH method using two types of matching criteria, a total score as the matching criterion and an attribute profile as the matching criterion. Finally, a statewide mathematics test was used to illustrate the implementation and possible limitations of the new method.