The Rasch model, named after the Danish mathematician Georg Rasch, is a statistical model used in the field of psychometrics to analyze data related to measurements of individuals' abilities, traits, or attributes. The primary purpose of the Rasch model is to assess how well a set of items (questions, tasks, or statements) measures a latent trait or ability that individuals possess, such as intelligence, reading comprehension, or a specific skill.
The Rasch model is often applied to educational testing, social sciences, health assessments, and various other fields where quantifying latent traits is important. It's used to develop and evaluate measurement instruments (like tests or questionnaires) by ensuring that the items are reliable, valid, and capable of effectively differentiating between individuals with different levels of the latent trait.
The Rasch or 1-parameter logistic item response theory (IRT) model is a unidimensional measurement model for binary and ordinal response variables (e.g., test and questionnaire items) that implies equal discrimination (slopes of the logistic function or item characteristic curves) across items. That is, the items are assumed to measure a single latent trait variable (factor) and to only differ in their difficulty (location) but not their discrimination (slope).
The Rasch model can be used to test whether a set of items measures a single common latent variable with equal discrimination. A related unidimensional IRT model is the Birnbaum or 2-parameter logistic model which relaxes the assumption regarding equal item discrimination.
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