Umean (user mean and scale and decimal places) = 0, 1, 2
The standard unit of measurement is the logit (log-odds unit). These measurement units are inconvenient for reporting results to examinees, parents, administrators etc. They can be linearly rescaled to make the reported results more useful to the user. The standard origin (mean) is the mean of the item difficulties, the standard scaling is 1, i.e., 1 reported unit per logit. These values may be changed by
Umean = user origin value, user units per logit, decimal places to report
also, for convenience, these can be specified separately
Uscale = user units per logit
Udecimals = user decimal places
Anchoring and Umean=
It is always safest to include the Umean= (mean),(logit scaling) of the analysis that produced the anchor values.
A useful transformation is to take the high and low measures on the vertical rulers in Table 6.0 or Table 7 and assign that range to 0-100. Then linearly transform all other measures.
Suppose the highest measure is +8.0 logits and the lowest measure is -7.0 logits on Table 6.0 of an analysis. This gives a range of 15 logits, i.e., 100/15 = 6.67 points per logit.
For reporting purposes, transform all measures by Measure* 6.67 + 46.7 and report with 1 decimal place.
Umean = 7, 6.67, 1
A measure of +2.0 logits becomes 2+*6.67 + 46.7 = 60.0 user-scaled points
Standard errors become (Standard error logits) * 6.67.
A standard error of .03 logits becomes (.03)*6.67 = .2 user-scaled points
Example 2: Set the origin of the measurement scale at 50 units, with 10 units per logit, and report 0 decimal places. This usually gives a measure range somewhat like 0-100.
Umean = 50, 10, 0
Example 3: From an earlier run, the lowest person measure is -6.23 logits, and highest 7.45 logits. Rescale so that the person measure range is 0 - 100.
The new scale is 100 units. The old range was 6.23 + 7.45 = 13.68 logits, so scaling factor = 100 / 13.68 = 7.31 units per logit.
The new origin is offset 6.23 logits = 6.23*7.31 units = 45.54 units
Umean = 45.54, 7.31 ; the standard number of decimal places, 2, is reported.
Example 4: You wish to treat an element as a dummy. It is used for selection, fit analysis and bias detection only.
If Umean = 0 (the standard)
1=dummy element,0 ; anchor this at the umean= value
If Umean = 50 (user setting)
1=dummy element,50 ; anchor this at the umean= value
Example 5: -5 to +3 is to be reported as 0 to 25.
Usually the "previous Umean=" is zero.
The computation generally is:
Existing range of measures = -5 to +3 (or whatever is in your Facets report)
Desired range = 0 to 25
Scaling = (25 - 0) / (3 - -5) = 25/8 = 3.125
Umean= is given by equivalent values: 25 matches 3
New value = old value * scaling + Umean
25 = 3.125 * 3 + Umean
Umean = 15.625
So that the Facets specification is:
Umean = 15.625, 3.125
Checking this for the 0 point:
0 = -5*3.125 + 15.625
Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
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|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 with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind||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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|Coming Rasch-related Events|
|Jan. 5 - Feb. 2, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Jan. 10-16, 2018, Wed.-Tues.||In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement|
|Jan. 17-19, 2018, Wed.-Fri.||Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website|
|Jan. 22-24, 2018, Mon-Wed.||In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx|
|April 10-12, 2018, Tues.-Thurs.||Rasch Conference: IOMW, New York, NY, www.iomw.org|
|April 13-17, 2018, Fri.-Tues.||AERA, New York, NY, www.aera.net|
|May 22 - 24, 2018, Tues.-Thur.||EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 27 - 29, 2018, Wed.-Fri.||Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org|
|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|July 25 - July 27, 2018, Wed.-Fri.||Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org|
|Aug. 10 - Sept. 7, 2018, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Sept. 3 - 6, 2018, Mon.-Thurs.||IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org|
|Oct. 12 - Nov. 9, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
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