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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
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 ...
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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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Dynamic game difficulty balancing (DGDB), also known as dynamic difficulty adjustment (DDA), adaptive difficulty or dynamic game balancing (DGB), is the process of automatically changing parameters, scenarios, and behaviors in a video game in real-time, based on the player's ability, in order to avoid making the player bored (if the game is too easy) or frustrated (if it is too hard).