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Simulation Study I: The average loss for configuration recovery when J increases from 200 to 1000. For each J, the table shows the 25%, 50% and 75% quantiles of the loss based on 100 independent experiments.
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Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal points, with person-person, item-item, and person-item similarities being captured by the Euclidian distances...
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Context 1
... this table, we see that the loss tends to decrease as the sample size increases, supporting the result of Proposition 3. Table 2 presents the results on loss (3) for configuration recovery, where the best isometry mapping F in (3) is obtained by solving an optimization problem given the true and estimated ideal points. Similar to the results on partial distance matrix recovery, the loss (3) also decreases towards 0 as J grows large, which is consistent with the result of Theorem 3. ...Context 2
... this table, we see that the loss tends to decrease as the sample size increases, supporting the result of Proposition 3. Table 2 presents the results on loss (3) for configuration recovery, where the best isometry mapping F in (3) is obtained by solving an optimization problem given the true and estimated ideal points. Similar to the results on partial distance matrix recovery, the loss (3) also decreases towards 0 as J grows large, which is consistent with the result of Theorem 3. ...