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IRT is a framework for designing, analyzing, and scoring tests, questionnaires, and similar instruments that measure abilities, aptitudes, or traits. It emphasizes the relationship between the latent trait under examination and the probability of a given response.

In IRT, a latent trait is an unobservable characteristic or attribute such as ability or personality, which the test is designed to measure.

The ICC is a graph that plots the probability of a correct response to an item against the latent trait level of the examinee.

The item difficulty parameter in IRT indicates the point on the latent trait scale at which an item has a 50% chance of being answered correctly. A higher value means that the item is more difficult.

This is a measure of how well an item can differentiate between respondents with differing levels of the latent trait. A higher a-parameter indicates better discrimination.

In IRT, the guessing parameter accounts for the likelihood that a respondent will answer an item correctly by guessing. This is particularly relevant in multiple-choice items.

Theta is a symbol often used to represent the latent trait level of an individual in IRT models.

The 3PL model in IRT incorporates three parameters: item difficulty (b), item discrimination (a), and guessing (c), to explain the probability of a correct response.

The 2PL model is a version of IRT that includes only two parameters: item difficulty (b) and item discrimination (a), without considering the guessing factor.

Also known as the Rasch model, the 1PL assumes that all items have the same discrimination parameter (a) and only the difficulty (b) parameter varies among items.

TIF in IRT shows the amount of information that a test or a set of items provides across different levels of the latent trait. Higher information implies more precision in measuring the trait.

This assumption in IRT states that a test measures a single latent trait or ability. All items on the test contribute to assessing this one dimension.

In IRT, the assumption of local independence means that responses to items are independent of each other given the latent trait level of the individual.

Scaling involves converting raw test scores onto a scale that represents the latent trait (usually theta) using an IRT model.

DIF occurs when items on a test have different probabilities of a correct response for individuals of the same ability level but different subgroups (e.g., gender, ethnicity).

Model fit in IRT examines the extent to which the data collected fits the chosen IRT model, indicating how well the model describes the performance of items.

MLE in IRT is a statistical method used to estimate the parameters of the IRT model that maximize the likelihood of the observed set of responses.

Unlike MLE, Bayesian estimation in IRT involves prior distributions for parameters and uses Bayes' theorem to update parameter estimates given the data.

EAP is a Bayesian estimation technique in IRT that produces point estimates of ability for examinees by taking a weighted average, where the weights are the posterior probabilities.