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The accumulator model proposed by Vickers and the modified random-walk model proposed by Link and Heath are compared in their ability to account for confidence judgments in line-length discrimination tasks. The random-walk model proves to be a viable alternative to the accumulator model, and is able to account for the relationship between mean response time and confidence. The parameter estimation techniques available for the random-walk model are considered advantageous when compared with the accumulator model, because the predictions from the latter have been obtained with the use of computer simulation.