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 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 2nd. 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 |
|
|
|
| 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 | |
|---|---|
| June 19-21, 2013, Wed.-Fri. | SIS 2013 Conference on Advances in Latent Variables: Methods, Models and Applications, Brescia, Italy, meetings.sis-statistica.org/index.php/sis2013/ALV |
| July 1 - Nov. 30, 2013, Mon.-Sun. | Online Course: Introduction to Rasch Measurement Theory (D. Andrich, RUMM), www.education.uwa.edu.au/ppl/courses |
| July 5 - Aug. 2, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| July 15, 2013, Monday | Application deadline: UIC Educational Research Methodology online graduate certificate program, www.go.uic.edu/OnlineMESA |
| July 22, 2013, Monday | Submission deadline: 2014 AERA Annual Meeting, Philadelphia PA, www.aera.net |
| Aug.1-5, 2013, Thur.-Mon. | TERA-PROMS Annual Meeting, Kaohsiung, Taiwan, tera.education.nsysu.edu.tw |
| Aug. 9 - Sept. 6, 2013, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Aug. 22, 2013, Thursday. | Symposium in honor of Svend Kreiner, Copenhagen, Denmark, biostat.ku.dk/kreinersymposium |
| Sept. 4-6, 2013, Wed.-Fri. | IMEKO TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences, Genoa, Italy, www.imeko-genoa-2013.it |
| Sept. 13 - Oct. 11, 2013, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 18-20, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 23-25, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 26-27, 2013, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Oct. 18 - Nov. 15, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
| Oct. 20 - Oct. 25, 2013, Sun.-Fri. | International Association for Educational Assessment (IAEA) 39th Annual Conference, Tel Aviv, Israel, www.iaea-2013.com |
| Dec. 11-13, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| March 12-14, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| April 3-7, 2014, Thurs.-Mon. | AERA Annual Meeting, Philadelphia PA, www.aera.net |
| May 14-16, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| May 19-21, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| July 4 - Aug. 1, 2014, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| Aug. 8 - Sept. 5, 2014, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Sept. 10-12, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 12 - Oct. 10, 2014, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 15-17, 2014, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 18-19, 2014, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| The javascript to add "Coming Rasch-related Events" to your webpage is: <script type="text/javascript" src="http://www.rasch.org/events.txt"></script> | |
The URL of this page is www.rasch.org/rmt/rmt211h.htm
Website: www.rasch.org/rmt/contents.htm