1. A Mixture Rasch Model-Based Computerized Adaptive test for Latent Class identification Hong Jiao, George Macredy, Junhui Liu, & Youngmi Cho (2012)

2. The Mixture Rasch Model

3. The Implementation of a Mixture Rasch Model-Based CAT • Starting Point (first item) • “Best guess”, “Use what you’ve got”, or “Start easy”. • Selecting five items randomly from the calibration item pool • Item Selection Algorithm • Fisher information • Kullback-Leibler (KL) information • Termination Rule • Fixed-length • Fixed-precision

4. KL information • The latent trait measured within each latent class is unidimensional but the latent traits measured across latent classes are multidimensional. • Estimation of ability parameters • One single latent ability parameter • Class-specific ability parameters

5. Method 1 • Estimation of a single latent ability parameter, to maximize the KL information between two latent classes at the current ability estimate. • Maximizes the information to distinguish between the latent classes conditional on the current ability estimate. • Appropriate for used when the same latent ability is measured across latent classes.

6. Method 2 • Estimation of a single latent ability parameter, to maximize the distinction between latent classes as well as between the current ability estimate and its true value. • Maximizes the information to distinguish between both latent classes and the upper and lower bounds of the interval set around the current ability estimate. • Appropriate for used when the same latent ability is measured across latent classes.

7. Method 3 • Estimation of one latent ability for each latent class, to maximize the distinction between latent classes and between current ability estimates for each latent class. • No interim latent class membership updating.

8. Method 4 • Combine Method 1 and 3, is a sum of the weighted KL information based on each class-specific ability estimate makes use of all possible sources of information • Only appropriate for use when the same latent trait us measured across the two classes.

9. Method • 12 Item selection methods

10. Memberships: 2; 5000 examinees for each class. • Four item pools, each with 500 items. • Mixing proportion: 50% for both latent classes. • Test length: 20-item

11. Ability estimation • For Method 1 & 2: a single ability estimate across classes. • Administration of item  estimated a latent class membership  estimated ability parameter. • Sequentially administered item and updated latent class membership and ability parameter. • For Method 3 & 4: class-specific ability estimates. • Administration of item  estimated class-specific ability parameters. • Sequentially administered item and updated ability parameters. • The latent class membership only estimated when the last item was administered.

12. Results

20. The distribution of the converged posterior classification decisions as a function if item sequence (5-20) in the CAT administration. • The classification became stabilized or converged for more than 70% of the examinees after administration of the first five items.

21. The number of examinees whose classification converged at Item 5 was smaller than that for Pool 1, due to less KL information provided by Pool 2. • All alternatives under Method 2 required fewer items to produce stable classification decisions for a majority of the examinees.

22. Questions • If more than two latent classes involve in the test, are these KL methods still workable? • To consider mixture model in computerized classification test. • Why the random item selection yielded significantly the most accurate estimates of person ability, compared to the proposed four methods. • The speedness behavior is a kind of latent class. To add this condition by setting the only last several items with latent class model.