Difference to CTT

Classical Test Theory (CTT) - analyses are the easiest and most widely used form of analyses

Most of tests are constructed based on CTT

Classical Analyses are performed on the test rather than on the item and although item statistics can be generated - Test reliability, test validity

What does IRT do differently in comparison to CTT

IRT/latent trait models aim to look beyond that at the underlying traits which are producing the test performance. They are measured at item level

Basically, a logistic regression of P(1) on the latent trait

IRT refers to a family of latent trait models used to establish psychometric properties of items and scales

Components of IRT (3)

Item response function (IRF) – Mathematical function relating the latent trait to the probability of endorsing an item

Invariance – position on the latent trait can be estimated by any items with known IRFs. Item characteristics are population independent

Item Information Function – an indication of item quality; an item’s ability to differentiate among respondents

Item Response Function

Item Response Function (IRF) - characterizes the relation between a latent variable (i.e., individual differences on a construct) and the probability of endorsing an item.

The IRF models the relationship between examinee trait level, item properties and the probability of endorsing the item.

Examinee trait level is signified by the Greek letter theta (0-)

Dichotomous case

• The problem: Dependent variable is binary, with a yes or a no answer

• Can be coded, 1 for yes and 0 for no

• There are no other valid responses

Item responde function

graphic

Solution: Use a Different Functional Form

The properties we need

The model should be bounded by 0 and 1

The model should estimate a value for the dependent variable in terms of the probability of being in one category or the other

Item response function

Different functional form

Solution: Use a Different Functional Form cont.

We want to know the probability, p, that a particular case falls in the 0 or the 1 category

We want to derive a model which gives good estimates of 0 and 1, or put another way, that a particular case is likely to be a 0 or a 1

- Thus, modelling the probability of correctly answering a dichotomously scored item means predicting the probability of getting it right conditional on the latent trait theta (q)

Item response function => logistic curve

item difficulty

Item difficulty

An item’s location is defined as the amount of the latent trait needed to have a .5 probability of endorsing/solving the item

The higher the “delta” parameter the higher on the trait level a respondent needs to be in order to endorse/solve the item

item discrimination

Item discrimination

Indicates the steepness of the IRF at the item’s location

An items discrimination indicates how strongly related the item is

to the latent trait like loadings in a factor analysis

Items with high discriminations are better at differentiating

respondents around the location point; small changes in the

latent trait lead to large changes in probability

Vice versa for items with low discriminations

Last changed3 months ago