A Mixture Rasch Model-Based Computerized Adaptive test for Latent Class identification

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 Implementation of a Mixture Rasch Model-Based CAT

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

KL information

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Estimation of a single latent ability parameter, to maximize the KL information between two latent classes at the current ability estimate.◦

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Method 1

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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.◦

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Method 2

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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.

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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.

Method 4

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12 Item selection methods

Method

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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 separation

Small item separation

Large ability separation Pool 1 Pool 2Small ability separation Pool 3 Pool 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.

Results

•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.

Questions