Practical Adaptive Testing CAT Algorithm

Here are the core steps needed for practical adaptive testing with the Rasch model.

0. Request next candidate: Set D=0, L=0, H=0, and R=0.
1. Find next item near difficulty (D).
2. Set D at the actual calibration of that item.
3. Administer that item.
4. Obtain a response.
5. Score that response.
6. Count the items taken: L = L + 1
7. Add the difficulties used: H = H + D
 
If response not correct,
8. Target next item difficulty: D = D - 2/L
 
If response correct,
9. Count right answers: R = R + 1
10. Target next item difficulty: D = D + 2/L
 
If not ready to decide to pass/fail,
11. Go to step 1.
 
If ready to decide pass/fail,
12. Calculate wrong answers: W = L - R
13. Estimate measure: B = H/L + log_e(R/W)
If W = 0 then B = H/L + log_e(R-0.5 / W+0.5)
If R = 0 then B = H/L + log_e(R+0.5 / W-0.5)
For a more precise estimate of B, see Estimating Measures with Known Item Difficulties  
14. Estimate Error: S = sqrt[L/(R*W)]
If W = 0 then S = sqrt[L/(R-0.5 * W+0.5)]
If R = 0 then S = sqrt[L/(R+0.5 * W-0.5)]
 
15. Compare measure B with pass/fail standard T.
16. If (T - S) < B < (T + S), go to step 1.
17. If (B - S) > T, then pass.
18. If (B + S) < T, then fail.
20. Go to step 0.

Practical adaptive testing. Wright BD. … Rasch Measurement Transactions 2:2 p.24

Practical adaptive testing. Wright BD. … Rasch Measurement Transactions, 1988, 2:2 p.24

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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