Estimating Rasch (person, ability, theta) Measures with Known Dichotomous Item Difficulties: Anchored Maximum Likelihood Estimation (AMLE)

For polytomies, see

Once item difficulties (criterion-referenced or norm-referenced) have been carefully calibrated and the measurement system constructed, we can administer some or all of the calibrated items to further examinees and measure them based on the pre-calibrated item difficulties. The approach here obtains the maximum-likelihood estimates using Newton-Raphson iteration.

For explanation, see Wright B.D., Douglas G.A. 1975. Best Test and Self-Tailored Testing. Research Memorandum #19. Chicago: MESA Press.

This estimation is implemented in Mark Moulton's Excel Spreadsheet.

Warm's (Weighted Mean) Likelihood Estimates (WLE)

For an explanation of WLE, see RMT (2009), 23:1, 1188-9

Warm's bias correction is applied to each MLE estimate, M, to produce a Warm's Mean Likelihood Estimate (WLE), MWLE, which is almost always closer to the mean item difficulty than M.

person n's WLE estimate = MWLE = M + ( J / ( 2 * I2 ) )
where, for dichotomous Rasch items,
J = Σ ( Pi (1-Pi ) (1-2Pi) ) summed over i = 1,L
I = Σ ( Pi (1-Pi ) )

summed over i = 1,L

Estimating Rasch (person, ability, theta) measures with known dichotomous item difficulties: Anchored Maximum Likelihood Estimation (AMLE). Wright B.D., Douglas G.A. … Rasch Measurement Transactions, 1996, 10:2 p.499

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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