Rasch model

The Rasch model, named after Georg Rasch, is a family of psychometric models for creating measurements from categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession and market research because of their general applicability. The Rasch model, named after Georg Rasch, is a family of psychometric models for creating measurements from categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession and market research because of their general applicability. The mathematical theory underlying Rasch models is a special case of item response theory and, more generally, a special case of a generalized linear model. However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates to the role of specific objectivity, a defining property of the Rasch model according to Georg Rasch, as a requirement for successful measurement. In the Rasch model, the probability of a specified response (e.g. right/wrong answer) is modeled as a function of person and item parameters. Specifically, in the original Rasch model, the probability of a correct response is modeled as a logistic function of the difference between the person and item parameter. The mathematical form of the model is provided later in this article. In most contexts, the parameters of the model characterize the proficiency of the respondents and the difficulty of the items as locations on a continuous latent variable. For example, in educational tests, item parameters represent the difficulty of items while person parameters represent the ability or attainment level of people who are assessed. The higher a person's ability relative to the difficulty of an item, the higher the probability of a correct response on that item. When a person's location on the latent trait is equal to the difficulty of the item, there is by definition a 0.5 probability of a correct response in the Rasch model. A Rasch model is a model in one sense in that it represents the structure which data should exhibit in order to obtain measurements from the data; i.e. it provides a criterion for successful measurement. Beyond data, Rasch's equations model relationships we expect to obtain in the real world. For instance, education is intended to prepare children for the entire range of challenges they will face in life, and not just those that appear in textbooks or on tests. By requiring measures to remain the same (invariant) across different tests measuring the same thing, Rasch models make it possible to test the hypothesis that the particular challenges posed in a curriculum and on a test coherently represent the infinite population of all possible challenges in that domain. A Rasch model is therefore a model in the sense of an ideal or standard that provides a heuristic fiction serving as a useful organizing principle even when it is never actually observed in practice. The perspective or paradigm underpinning the Rasch model is distinct from the perspective underpinning statistical modelling. Models are most often used with the intention of describing a set of data. Parameters are modified and accepted or rejected based on how well they fit the data. In contrast, when the Rasch model is employed, the objective is to obtain data which fit the model (Andrich, 2004; Wright, 1984, 1999). The rationale for this perspective is that the Rasch model embodies requirements which must be met in order to obtain measurement, in the sense that measurement is generally understood in the physical sciences.