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 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|
|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.
|Coming Rasch-related Events|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Jan. 22 -Feb. 19, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 21 -June 18, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 13 - Sept. 10, 2021, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith,Facets), www.statistics.com|
|June 24 - July 22, 2022, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt211h.htm