# Hong Jiao, George Macredy, Junhui Liu, & Youngmi Cho (2012)

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Hong Jiao, George Macredy, Junhui Liu, & Youngmi Cho (2012)

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 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

  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

 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.

 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.

 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.

 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.

 12 Item selection methods

 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 Large item separationSmall item separation Large ability separationPool 1Pool 2 Small ability separationPool 3Pool 4

 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.

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.

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.

 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.

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