The item response theory (latent trait theory) provides a way to model the probability that a person with X ability will be able to perform at level of Y. It models the probability that a person with X amount of a personality trait will exhibit Y amount of that trait on a test that is supposed to measure is. This theory focusses on the relationship between a testtaker’s response to an individual test item and that testtaker’s standing on the construct being measured.

Discrimination signifies the degree to which an item differentiates among people with higher or lower levels of the trait. Items can be given different weight in the item response theory. In classical test theory, there are no assumptions about the frequency distribution of test scores.

There are several assumptions of the item response theory:

1. Unidimensionality
   This assumption states that the set of items measures a single continuous latent construct. This assumption does not neglect minor dimensions, although assumes one dominant dimension underlying the structure.
2. Local independence
   This assumption states that there is a systematic relationship between all of the test items and this relationship has to do with the level of a person on the construct of interest. If this assumption is met, then the differences in responses to items are reflective of differences in the underlying trait or ability.
3. Monotonicity
   This assumption states that the probability of endorsing or selecting an item response indicative of higher levels of the construct should increase if as the level of the underlying construct increases.

Local dependence refers to the fact that items can be dependent on another factor than what the test as a whole is measuring. Locally dependent items have higher inter-item correlations and it may be controlled for by combining the responses to a set of locally dependent items into a separate subscale within the test. The theta level refers to the level of the underlying construct.

The probabilistic relationship between a testtaker’s response to a test item and that testtaker’s level on the latent construct being measured can be expressed in the item characteristic curve (ICC).

IRT enables test users to better understand the range of the underlying construct for which an item is most useful in discriminating among groups of testtakers. This can be done using the information function.

Information refers to the precision of measurement.

Items with low information prompt the test developer to consider the possibility that the content of the item does not match the construct measured by the other items (1), the item is poorly worded (2), the item is too complex (3), the placement of the item in the test is out of context (4) or cultural factors may be operating to weaken the item’s ability to discriminate between groups (5).