Rasch Analysis
Rasch analysis is a family of measurement procedures based on the model proposed by Danish mathematician Georg Rasch in 1960. The model expresses the probability of a correct response as a logistic function of the difference between a person's ability and an item's difficulty, both estimated on a single logit scale. Within item response theory it is equivalent to the one-parameter logistic (1PL) model; Rasch advocates argue that the model's properties of specific objectivity and parameter separability make it a measurement framework in its own right rather than one IRT option among several.
Model and properties
For a dichotomous item, the probability of a correct response is
P(X = 1 | θ, b) = exp(θ − b) / (1 + exp(θ − b))
where θ is the person parameter and b the item difficulty. Item discrimination is fixed at 1 across items and no guessing parameter is included. When data fit the model, person measures are independent of the particular items administered and item measures independent of the particular persons sampled — the property Rasch called specific objectivity. Sufficiency of raw scores for ability estimation follows from the same algebra.
Practice
Rasch analyses report person and item parameters in logits, item and person separation reliabilities, and infit and outfit mean-square statistics that flag misfitting items or examinees. Polytomous extensions — the rating scale model and the partial credit model — handle ordered category responses and dominate scale construction in attitude and language-learning research. Multifaceted extensions feed into the many-facet Rasch model for performance assessments.
In language testing, Rasch analysis is used for item banking, equating across forms, DIF detection, and cut-score setting. Cambridge English assessments and the Pearson Test of English use Rasch-based item banks; the Common European Framework of Reference's anchoring procedures draw on Rasch scaling.
References
- Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research.
- Bond, T. G., & Fox, C. M. (2015). Applying the Rasch Model: Fundamental Measurement in the Human Sciences (3rd ed.). Routledge.
- McNamara, T. (1996). Measuring Second Language Performance. Longman.