# Item Response Analysis Task

An Item Response Analysis Task is an analysis task to induce an item-level model.

**Context:**- It can be solved by a Item Response Analysis System (that implements an Item Response Analysis Algorithm).

**See:**High-Stakes Test, Test-Level Model, Linear Fixed-Effect Model, Linear Mixed-Effect Model.

## References

### 2013

- http://en.wikipedia.org/wiki/Item_response_theory
- In psychometrics,
**item response theory**(IRT) also known as**latent trait theory**, strong true score theory, or**modern mental test theory**, is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. Unlike simpler alternatives for creating scales as the simple sum questionnaire responses it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, the assumption in Likert scaling that “*All items are assumed to be replications of each other or in other words items are considered to be parallel instruments*”^{[1]}(p. 197). By contrast, item response theory treats the difficulty of each item (the ICCs) as information to be incorporated in scaling items.It is based on the application of related mathematical models to testing data. Because it is generally regarded as superior to classical test theory, it is the preferred method for developing scales, especially when optimal decisions are demanded, as in so-called high-stakes tests e.g. the Graduate Record Examination (GRE) and Graduate Management Admission Test (GMAT).

The name

*item response theory*is due to the focus of the theory on the item, as opposed to the test-level focus of classical test theory. Thus IRT models the response of each examinee of a given ability to each item in the test. The term*item*is generic: covering all kinds of informative item. They might be multiple choice questions that have incorrect and correct responses, but are also commonly statements on questionnaires that allow respondents to indicate level of agreement (a rating or Likert scale), or patient symptoms scored as present/absent, or diagnostic information in complex systems.IRT is based on the idea that the probability of a correct/keyed response to an item is a mathematical function of person and item parameters. The person parameter is construed as (usually) a single latent trait or dimension. Examples include general intelligence or the strength of an attitude. Parameters on which items are characterized include their difficulty (known as "location" for their location on the difficulty range), discrimination (slope or correlation) representing how steeply the rate of success of individuals varies with their ability, and a pseudoguessing parameter, characterising the (lower) asymptote at which even the least able persons will score due to guessing (for instance, 25% for pure chance on a 4-item multiple choice item).

- In psychometrics,

### 2007

- (Johnson, 2007) ⇒ Matthew S. Johnson. (2007). “Marginal Maximum Likelihood Estimation of Item Response Models in R.” In: Journal of Statistical Software, 20(10).
- ABSTRACT: Item response theory (IRT) models are a class of statistical models used by researchers to describe the response behaviors of individuals to a set of categorically scored items. The most common IRT models can be classified as generalized linear fixed- and/or mixed-effect models. Although IRT models appear most often in the psychological testing literature, researchers in other fields have successfully utilized IRT-like models in a wide variety of applications. This paper discusses the three major methods of estimation in IRT and develops R functions utilizing the built-in capabilities of the R environment to find the marginal maximum likelihood estimates of the generalized partial credit model. The currently available R packages ltm is also discussed.

### 1981

- (Bock & Aitkin, 1981) ⇒ R Darrell Bock, and Murray Aitkin. (1981). “Marginal Maximum Likelihood Estimation of Item Parameters: Application of An EM Algorithm.” In: Psychometrika. doi:10.1007/BF02293801
- QUOTE: Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used.