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Item response theory. Thissen, David and Lynne Steinberg. Roger E.

Millsap and Alberto Maydeu-Olivares. SAGE Knowledge. Have you created a personal profile? Login or create a profile so that you can create alerts and save clips, playlists, and searches. Please log in from an authenticated institution or log into your member profile to access the email feature. Item response theory IRT is a collection of mathematical models and statistical methods used for two primary purposes: item analysis and test scoring. Subsidiary uses of IRT include the design and assembly of tests and questionnaires, and the investigation of the structure of cognitive and affective constructs.

IRT is used with data arising from educational tests of ability, proficiency or achievement as well as psychological questionnaires measuring attitudes or personality traits or states. As a tool for item analysis, IRT makes explicit the fact that many tests and questionnaires are intended to measure individual differences on some unobserved, or latent , construct.

CQ Press Your definitive resource for politics, policy and people. Remember me? Back Institutional Login Please choose from an option shown below. Need help logging in? As with any use of mathematical models, it is important to assess the fit of the data to the model. If item misfit with any model is diagnosed as due to poor item quality, for example confusing distractors in a multiple-choice test, then the items may be removed from that test form and rewritten or replaced in future test forms.

If, however, a large number of misfitting items occur with no apparent reason for the misfit, the construct validity of the test will need to be reconsidered and the test specifications may need to be rewritten.


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Thus, misfit provides invaluable diagnostic tools for test developers, allowing the hypotheses upon which test specifications are based to be empirically tested against data. There are several methods for assessing fit, such as a Chi-square statistic , or a standardized version of it. Two and three-parameter IRT models adjust item discrimination, ensuring improved data-model fit, so fit statistics lack the confirmatory diagnostic value found in one-parameter models, where the idealized model is specified in advance.

Data should not be removed on the basis of misfitting the model, but rather because a construct relevant reason for the misfit has been diagnosed, such as a non-native speaker of English taking a science test written in English. Such a candidate can be argued to not belong to the same population of persons depending on the dimensionality of the test, and, although one parameter IRT measures are argued to be sample-independent, they are not population independent, so misfit such as this is construct relevant and does not invalidate the test or the model.

Such an approach is an essential tool in instrument validation.


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In two and three-parameter models, where the psychometric model is adjusted to fit the data, future administrations of the test must be checked for fit to the same model used in the initial validation in order to confirm the hypothesis that scores from each administration generalize to other administrations. If a different model is specified for each administration in order to achieve data-model fit, then a different latent trait is being measured and test scores cannot be argued to be comparable between administrations.

One of the major contributions of item response theory is the extension of the concept of reliability. Traditionally, reliability refers to the precision of measurement i. Traditionally, it is measured using a single index defined in various ways, such as the ratio of true and observed score variance. This index is helpful in characterizing a test's average reliability, for example in order to compare two tests.

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But IRT makes it clear that precision is not uniform across the entire range of test scores. Scores at the edges of the test's range, for example, generally have more error associated with them than scores closer to the middle of the range.

Selecting optimal screening items for delirium: an application of item response theory

Item response theory advances the concept of item and test information to replace reliability. Information is also a function of the model parameters. For example, according to Fisher information theory, the item information supplied in the case of the 1PL for dichotomous response data is simply the probability of a correct response multiplied by the probability of an incorrect response, or,.

The standard error of estimation SE is the reciprocal of the test information of at a given trait level, is the. For other models, such as the two and three parameters models, the discrimination parameter plays an important role in the function. The item information function for the two parameter model is. In general, item information functions tend to look bell-shaped. Highly discriminating items have tall, narrow information functions; they contribute greatly but over a narrow range.

Less discriminating items provide less information but over a wider range. Plots of item information can be used to see how much information an item contributes and to what portion of the scale score range.

Item response theory

Because of local independence, item information functions are additive. Thus, the test information function is simply the sum of the information functions of the items on the exam. Using this property with a large item bank, test information functions can be shaped to control measurement error very precisely. Characterizing the accuracy of test scores is perhaps the central issue in psychometric theory and is a chief difference between IRT and CTT. These results allow psychometricians to potentially carefully shape the level of reliability for different ranges of ability by including carefully chosen items.

For example, in a certification situation in which a test can only be passed or failed, where there is only a single "cutscore," and where the actual passing score is unimportant, a very efficient test can be developed by selecting only items that have high information near the cutscore. These items generally correspond to items whose difficulty is about the same as that of the cutscore.

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The estimate of the person parameter - the "score" on a test with IRT - is computed and interpreted in a very different manner as compared to traditional scores like number or percent correct. The individual's total number-correct score is not the actual score, but is rather based on the IRFs, leading to a weighted score when the model contains item discrimination parameters. A graph of IRT scores against traditional scores shows an ogive shape implying that the IRT estimates separate individuals at the borders of the range more than in the middle.

An important difference between CTT and IRT is the treatment of measurement error, indexed by the standard error of measurement. All tests, questionnaires, and inventories are imprecise tools; we can never know a person's true score , but rather only have an estimate, the observed score. There is some amount of random error which may push the observed score higher or lower than the true score.


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Also, nothing about IRT refutes human development or improvement or assumes that a trait level is fixed. A person may learn skills, knowledge or even so called "test-taking skills" which may translate to a higher true-score. In fact, a portion of IRT research focuses on the measurement of change in trait level. Classical test theory CTT and IRT are largely concerned with the same problems but are different bodies of theory and entail different methods. Although the two paradigms are generally consistent and complementary, there are a number of points of difference:.

It is worth also mentioning some specific similarities between CTT and IRT which help to understand the correspondence between concepts. In particular:.

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Thus, if the assumption holds, where there is a higher discrimination there will generally be a higher point-biserial correlation. Another similarity is that while IRT provides for a standard error of each estimate and an information function, it is also possible to obtain an index for a test as a whole which is directly analogous to Cronbach's alpha , called the separation index. To do so, it is necessary to begin with a decomposition of an IRT estimate into a true location and error, analogous to decomposition of an observed score into a true score and error in CTT.

The standard errors are normally produced as a by-product of the estimation process. The separation index is typically very close in value to Cronbach's alpha. IRT is sometimes called strong true score theory or modern mental test theory because it is a more recent body of theory and makes more explicit the hypotheses that are implicit within CTT. This is a partial list, focusing on texts that provide more depth.

From Wikipedia, the free encyclopedia. Paradigm for the design, analysis, and scoring of tests. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. This section does not cite any sources.