Rasch Measurement Model

Requirements of the SLM of Rasch

• 1.
  Items are designed to be conceptually ordered by difficulty along an increasing continuum from easy to harder for the variable being measured.
• 2.
  In designing the items (using three as an example), one keeps in mind that person measures of the variable are conceptualized as being ordered along the continuum from low to high according to certain conditions. The conditions in this example are that persons with low measures will have a high probability of answering the easy items positively, and a low probability of answering the medium and hard items positively. Persons with medium measures will have a high probability of answering the easy and medium items positively, and a low probability of answering the hard items positively. Persons with high measures will have a high probability of answering the easy, medium, and hard items positively. These conditions are tested through a Rasch analysis.
• 3.
  Data are collected from persons on the items and scored dichotomously (0/1 or 1/2), as in, for example, wrong/right, no/yes, none/a lot, or disagree/agree.
• 4.
  Each item is represented by a number, estimated from the data that represent its difficulty (called an item parameter in the mathematical representation of the Rasch model) that does not vary for persons with different measures of the variable. Persons with different measures responding to the items have to agree on the difficulty of the items (such as easy, medium, and hard, as used in this example). If the persons do not agree on an item's difficulty, then this will be indicated by a poor fit to the measurement model, and then the item may be discarded as not belonging to a measure on this continuum.
• 5.
  Each person is represented by a number, estimated from the data that represent his or her measure of the variable (called a person parameter in the mathematical representation of the Rasch model) that does [Page 822]not vary for items of different difficulty along the continuum. If different items do not produce agreement on a person measure, then this will be indicated by a poor fit to the measurement model, and then one examines the person response pattern (and the items).
• 6.
  Rasch measurement models use a probability function that allows for some variation in answering items such that, for example, a person with a high attitude measure sometimes might give a low response to an easy item, or a person with a medium achievement measure sometimes might answer a hard item correctly. If the person response pattern shows too much disagreement with what is expected, then it may be that the person has not answered the items properly or consistently, and that person's results may be discarded, or the item may be too hard or too easy.

Equations for the Simple Logistic Model of Rasch

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