A Mixture Rasch ModelBased Computerized Adaptive Test for Latent Class
Identification
Hong Jiao, George Macready, Junhui Liu and Youngmi Cho
This study explores a CAT algorithm to facilitate classification of examinees into known latent classes based on responses to items adaptively selected from an item pool that has been calibrated using the mixture Rasch model.
STEPS:
1. randomly select 5 items
2. estimate class membership and latent ability by EAP
3. choose next time based on the adapted Kullback–Leibler (KL) information indices
4. stop——fixed length method
4 different item selection methods were proposed based on the KL information. The former two methods assume estimation of a single latent ability across all latent classes. The students are classed into different group according to their mean ability level. The latter two methods assume estimation of one latent ability for each latent class. Every student will have two class posterior probabilities, the group will be decided by the comparing the sum of the posterior probabilities for each class by the class-specific ability estimate. The KL information method was compared with the reversed and the adaptive information.
The simulation study was used for illustrated.
4 item pools: 500 items
Group1:N(0,1)/ 5000examinees
Group2:N(1,1) & N(0.5,1) /5000examinees
The results show that when item separation is large, the classification is more accurate. However the ability estimate will be affected. On the other side, when the ability separation is large, the estimation of ability parameter is more accurate，meanwhile the classification will be sacrifice. The use of KL，reversed KL, or the adaptive KL information did not have much impact on the results.
1 since the model inclines to choose the larger difficulty differences between the two latent classes, the item exposure control problem should be consider.
2 what will happen when the unidimensional assumption is violated in both group？
3 it mainly use the extent of ability to group subjects, what about the same ability with different strategies? Is it solved by CDM or be considered by another classification variables?
4 the relation to DIF？