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The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between the respondent's abilities, attitudes, or personality traits, and the item difficulty.
where = is the total raw score for person n, = is the total raw score for item i, N is the total number of persons and I is the total number of items. Solution equations are obtained by taking partial derivatives with respect to δ i {\displaystyle \delta _{i}} and β n {\displaystyle \beta _{n}} and setting the result equal to 0.
The graph showing the relation between the probability of a given category as a function of person location is referred to as a Category Probability Curve (CPC). An example of the CPCs for an item with five categories, scored from 0 to 4, is shown in Figure 1. Figure 1: Rasch category probability curves for an item with five ordered categories
The item-total correlation provides an index of the discrimination or differentiating power of the item, and is typically referred to as item discrimination. In addition, these statistics are calculated for each response of the oft-used multiple choice item, which are used to evaluate items and diagnose possible issues, such as a confusing ...
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IRT is based on the idea that the probability of a correct/keyed response to an item is a mathematical function of person and item parameters. (The expression "a mathematical function of person and item parameters" is analogous to Lewin's equation, B = f(P, E), which asserts that behavior is a function of the person in their environment.) The ...
This analysis consists of computation of item difficulties and item discrimination indices, the latter index involving computation of correlations between the items and sum of the item scores of the entire test. If items that are too difficult, too easy, and/or have near-zero or negative discrimination are replaced with better items, the ...
Differential item functioning (DIF) is a statistical property of a test item that indicates how likely it is for individuals from distinct groups, possessing similar abilities, to respond differently to the item. It manifests when individuals from different groups, with comparable skill levels, do not have an equal likelihood of answering a ...