Abstract:
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In educational testing, inferences on ability have been mainly based on item responses while the time taken to complete an item are often ignored . With the advent of computerized testing, information on response time of each item can be obtained without additional cost. To better infer latent ability, a new class of state space models, conjointly modeling response time with time series of dichotomous responses, is put forward. The proposed models can entertain longitudinal observations at individually-varying and irregularly-spaced time points and can accommodate changes in ability and other complications, such as local dependence and randomized item difficulty. Simulations for the proposed models demonstrate that the biases of ability estimation are reduced and their precisions are improved. In applying the models to a large collection of reading test data from MetaMetrics company, we further investigated two competitive relationship in modeling response times with the distance of ability and item difficulty (i.e.monotone or inverted U-shape). The model comparison result supports the inverted U-shape relationship better captures examinees' behaviors and psychology in exams.
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