Warm's Mean Weighted Likelihood Estimates (WLE) of Rasch Measures

For a mathematical description of WLE, see RMT (2009), 23:1, 1188-9

Ronald A. Fisher (1922) formulated the concept of the likelihood of the data given a statistical model that is hypothesized to have generated those data and a set of parameter estimates. Maximum likelihood estimates are the parameters values which maximize the likelihood that the observed data would have been generated. Thus MLE values correspond to the mode of the likelihood function.

Thomas Warm (1989) points out the that those modal estimates are biased when viewed from the likelihood function as whole. He suggests that, rather than the mode of the likelihood function, estimates should be based on its mean. These estimates have come to be called "Warm estimates", and his approach is Warm (or Weighted) (Mean) Likelihood Estimation (WLE or WMLE).

In the Rasch model, the estimation of MLE and WLE require iteration. WLE is more computationally intensive. Warm demonstrates that the asymptotic variance of MLE and WLE estimates are the same, meaning that the estimates have the same model standard errors.

WLE estimates are generally slightly more central than MLE estimates, though the implications of this for practical applications are not clear, because the difference is usually less than the standard error of the estimates.

Fisher R.A., (1922) "On the mathematical foundations of theoretical statistics" Philosophical Transactions of the Royal Society of London (A) 222, 1922, p. 309-368.

Warm T.A. (1989) "Weighted Likelihood Estimation of Ability in Item Response Theory." Psychometrika, 54, 427-450.

John Michael Linacre

Note: Winsteps and Facets do not use MMLE or WLE, because Winsteps and Facets embody the philosophy that:
1. transposing the data matrix (exchanging the persons and items) should impact estimation as little as possible.
2. estimating the person and item measures from a free analysis should produce the same results as (i) anchoring the items at their free estimates, and estimating the person measures, or (ii) anchoring the persons at their free estimates and estimating the item measures.

Warm's Mean Weighted Likelihood Estimates (WLE) of Rasch Measures. Warm T.A. … Rasch Measurement Transactions, 2007, 21:1 p. 1094

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
Rasch Books and Publications: Winsteps and Facets
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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	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
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

Forum

Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

The URL of this page is www.rasch.org/rmt/rmt211h.htm

Website: www.rasch.org/rmt/contents.htm