Abstract
The DIF-Free-Then-DIF (DFTD) procedure, one method of assessing differential item functioning (DIF), has two stages: anchor item selection and DIF detection. Firstly, items that most likely to be DIF-free are located using a rank based approach. In the following stage, these assumed DIF-free items will be used as anchors to build a common scale for DIF assessment to the rest of the items. In addition, including more anchor items in stage 1 will yield higher hit rate and type I error rate in Stage 2 (Wang, 2004). However, anchor items will not be tested in Stage 2. Thus, in the present study, a new procedure inspired by Chen, Wang & Shih (2013) called double purification (DOP) has been provided to overcome the disadvantage of DFTD. On the other hand, in large scale assessments, items are restructured in several booklets so that every item, including anchor items, won__t be responded by every test participant. When we use DFTD in this __designed missing__ condition, it may yield a worse result than in the fully responded conditions because the information brought by anchor items will actually be less. Fortunately, the DOP method overcomes this difficulty by utilizing more anchor items without losing the chance to assessment them for DIF. A simulation study using the real item parameters from PISA2009 math subscale showed that DOP is superior to DFTD in the designed missing condition. Meanwhile, a real data example consisted of the same PISA2009 Taiwan samples had showed some inconsistencies from both results.