4.8 Why take the Rasch model?

• Invariant measurement: The Rasch model meets the five Engelhard criteria (c.f. Section 4.7).
• Interval scale: When it fits, the Rasch model provides an interval scale, the de-facto requirement for any numerical comparisons (c.f. Section 3.4.1).
• Parsimonious: The Rasch model has one parameter for each item and one parameter for each person. The Rash model one of the most parsimonious IRT models, and can easily be applied to thousands of items and millions of persons.
• Specific objectivity: Person and item parameters are mathematically separate entities in the Rasch model. In practice, this means that the estimated difference in ability between two persons does not depend on the difficulty of the test. Also, the estimated differences in difficulties between two items do not depend on the abilities in the calibration sample. The property is especially important in the analysis of combined data, where abilities can vary widely between sources. See Rasch (1977) for derivations and examples.
• Unified model: The Rasch model unifies distinct traditions in measurement theory. One may derive the Rasch model from
  • Thorndike’s 1904 criteria
  • Guttman scalogram model
  • Ratio-scale counts
  • Raw scores as sufficient statistics
  • Thurstone’s scaling requirements
  • Campbell concatenation
  • Rasch’s specific objectivity
• Fits child development data: Last but not least, as we will see in Section 6, the Rasch model provides an excellent fit to child development milestones.