Item Response Theory

The central idea

Classical scoring often treats every item as contributing a similar fixed amount. IRT models the response to each item as a function of a latent trait. An item can therefore be more informative in one region of the trait scale than another.

For a binary item, the model estimates the probability of one response. For rating-scale or forced-choice items, extensions model several response categories or comparisons.

Common item parameters

Depending on the IRT model, an item may have parameters describing:

• location or difficulty: where on the trait scale responses tend to change;
• discrimination: how sharply the item distinguishes nearby trait levels;
• guessing or lower asymptote: a baseline response probability in some ability tests;
• thresholds: boundaries between ordered response categories.

Personality items are not “difficult” in the everyday sense. Location describes where endorsement becomes more likely.

Why IRT is useful for adaptive tests

At each step, a CAT can estimate which available item would provide the most information near the current trait estimate. It can also calculate conditional precision rather than assuming the same measurement error for every respondent.

Assumptions and limits

IRT requires a model that fits the response process, a suitably calibrated item bank, and enough evidence that items behave consistently across relevant groups. Model complexity does not guarantee validity. Poor item content remains poor content after sophisticated mathematics.