Formalizing dimension and response violations of local independence in the unidimensional Rasch model.

摘要: Local independence in the Rasch model can be violated two generic ways that are generally not distinguished clearly literature. In this paper we distinguish between a violation of unidimensionality, which call trait dependence, and specific statistical independence, response both violate local independence. Distinct algebraic formulations for dependence developed as violations dichotomous model, data simulated with varying degrees according to these formulations, then analysed assuming no violations. Relative case it is shown result opposite effects on unit scale manifested range standard deviation person locations. reduced; increased. Again, relative violation, also have separation index (analogous Cronbach's alpha reliability traditional test theory value construction): decreases dependence; increases dependence. A way accounting combine dependent items into higher-order polytomous item. This typically results decreased alpha, compared analysing discrete, independent items. occurs irrespective kind data, so further contributes being clearly. an attempt begin them statistically articulates model.