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Testlet Response Theory

A testlet or an item bundle refers to a group of interrelated items presented as a single unit. Often, a testlet consists of several items following a single stimulus. It is a commonly used test construction unit in large-scale assessments and often provides a context or situation for assessing knowledge, skills, and ability. Passages in reading comprehension tests, scenarios in science tests, and graphs and/or tables in math tests are such examples in practice. When items are constructed around such a common stimulus, items associated with the same stimulus are connected by the common context. Item connection or clustering may affect an examinee’s performance on those items due to the common contextual effects. Thus, local item dependence (LID) or testlet effects may be induced. When LID is present, an examinee’s response to an item may affect the examinee’s response to other items in the same testlet given the person and item parameters. Testlet response theory models these effects. This entry describes testlet response theory and its models then discusses the estimation methods of the model parameters.

Standard item response theory (IRT) models are not robust to the violation of the local item independence assumption. LID affects model parameter estimation, equating, and estimation of test reliability. Possible causes for LID include passage dependence, item chaining, explanation of previous answers such as clueing, item or response format (multiple-choice vs. constructed response items), scoring rubrics, fatigue, speededness, and practice effects. Passage dependence refers generally to item clustering around a common stimulus.

One method documented in the literature to account for LID among dichotomously scored items within a testlet is to treat it as a single super-item, score it polytomously, and apply polytomous item response models such as the partial credit model, the graded response models, or the generalized partial credit model. This method may lead to loss of information due to the sum of correct responses to the dichotomous items within a testlet thus reducing measurement precision. If items are scored polytomously, it is not practical to sum up the polytomous scores to get a giant polytomous super-item with even more item response categories.

Testlet Response Theory Models

Testlet effects can be conceptualized from multiple perspectives, an interaction between a testlet and persons, multidimensionality, or contextual effects of item groups on items nested within a testlet. In accordance with these conceptualizations, different testlet response theory models have been proposed.

Bayesian Random-Effects Testlet Model

Eric Bradlow, Howard Wainer, and Xiaohui Wang proposed a two-parameter Bayesian random-effects testlet model by incorporating a random-effect parameter into the unidimensional two-parameter item response model, indicating the interaction between a person and a testlet. Extensions of this model have been made to a three-parameter IRT model as well as to the graded response model.

Rasch Testlet Model

In another attempt to model testlet effects, Wen-Chung Wang and Mark Wilson proposed the Rasch testlet model as a special case of the multidimensional random coefficients multinomial logit model by including one more dimension or latent trait for each testlet. Essentially, each testlet introduces one additional dimension to an item. For each item, two latent traits are underlying the item performance for a specific examinee. These two latent traits are the general latent trait the test is intended to measure and the testlet-specific latent trait. For the items within the same testlet, the testlet-specific latent trait remains the same across these items. For different testlets, the testlet-specific latent traits will be different. If there are six testlets on a test, overall the test has seven dimensions, but for each item, it assesses two dimensions.

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