Assessing Local Dependence in Educational Performance ...

Asscssin$ Local Del~nClenc~ - 3ability estimation. They suggested that calibra~cl dependent itcrn parameters tended toov'er-estimatc the origirm[ itcrn parameters. Ability estimates ~'erc even less accurate as thedegree of dependence increased. Bell, Pattison, and Withers (1988) described a Ioglinearmodeling approach to examine local dependence of items within and between clusters.They found item dependence to be more marked within rather than between clusters, thatdependence was stronger in items ba.~:d on mathematical than on verbal material, and thatdependence increased with examinee ability.Wilson (1988) provides a proc~ure to assess local dependence of bioary itemswhen the responses fit a Rasch modcl and provides illustrations ba.~'d on 20 science items.First he calibrated binary items under the assumption of local independence. Next. hegrouped the binary itcms into clusters (i.e., what he called subtests or superitems) and thencalibrated via Masters' one-parameter Partial Credit model for i:x)lychotomous items(Masters, 1982_; Wright & Masters, 1982). Finally, he osserted local dependence whenthere were substantial discrepancies between the results of the two calibrations. Huynh(1993) provides a partial theoretical justification of the procedure proposed by Wilson.Finally, Yen (1984) proposed using the Q3 statistic to assess local dependenceunder assumptions of latent trait models. For an examinee with ability 0j on item j, let Xjbe the raw score, Ej be the expected score from a latent trait model, and let Dj = Xj - Ej bethe residual score. Then the Q3jj, index for itemsj andj' is the correlation between the tworesiduals Dj and D'j taken over all examinees. Yen noted that since item j is includedexplicitly in the raw score Xj and implicitly in the (estimated) expected score E, a negativebias is built into Q3. When local independence holds, Q3 is expected to be approximately-1/(n-l) where n is the number of binary items. Yen (in press) applied the Q3 statistic tostudy binary, and polychotomous items and found that the Q3 statistic performs adequatelyfor polychotomous items. However, the use of Q3 is limited to data which adequately fit alatent trait model.