Weighting items and persons 
There are circumstances in which certain items are to be given more influence in constructing the measures than others. For instance, certain items may be considered critical to the demonstration of competence. Though Winsteps supports several methods, IWEIGHT= is simplest for items, and PWEIGHT= for persons. Another approach is to replicate the data for particular items. This can be done with FORMAT= without changing the data file. Items can also be rescored from say, 01 to 02, but this makes variable maps difficult to interpret.
Unweighted and Weighted analysis: unweighted data is preferable for calibrating the Rasch items. This is because each observation is modeled to contribute one unit of independent statistical information. The effect of weighting is to distort the distribution of independent statistical information in the data. A practical approach is:
Step 1. Analyze the data without weighting. Investigate misfit, construct validity, etc.
Step 2. Weight the items. Compare the item calibrations with weighted and unweighted data to identify where there are discrepancies.
The true reliability of the measures is from the unweighted analysis. Weighting introduces an arbitrariness into the analysis. One solution is to adjust the weights to maintain the unweighted reliability = Ru. The reliability of the weighted analysis, using an initial set of weights, = Rw. We can then scale the weights using the SpearmanBrown Prophecy Formula: S = Ru * (1Rw) / ((1Ru)*Rw)). Multiply the initial set of weights by S. Then the weighted and unweighted reliabilities should be the same.
Standard errors and fit statistics: The weights applied to items or persons are used in computing the measure estimates, standard errors and fit statistics. When using significance tests with weighting, normalize the weights so that the total amount of independent statistical information in the data is not over or underinflated, i.e., when using PWEIGHT= with an observed sample size of N, multiply all PWEIGHT= values by N / (sum of all weights).
The standard is weights = 1.
When an item or person is weighted as 2, then the estimation acts as though that item or person appears twice in the data file.
When an item or person is weighted as 0, then that person does not influence the estimates, standard errors or fit statistics of other persons and items, but does have measure, standard error and fit statistics computed on all observations for itself. This is useful for evaluating pilot or offdimensional items, or measuring idiosyncratic persons.
Estimation with weighting
Observation = Xni
Expected value (computed using the Rasch model) = Eni
Accumulated raw score = Accumulated raw score = Xni * IWEIGHT * PWEIGHT
Accumulated expected score = Accumulated expected score = Eni * IWEIGHT * PWEIGHT
Accumulated marginal count for item = Accumulated marginal count for item + IWEIGHT * PWEIGHT
Accumulated marginal count for person = Accumulated marginal count for person + IWEIGHT * PWEIGHT
Special rules apply when IWEIGHT=0 or PWEIGHT=0.
IWEIGHT=0 the item totals are incremented by PWEIGHT. The person totals are not incremented.
PWEIGHT=0 the person totals are incremented by IWEIGHT. The item totals are not incremented.
JMLE Estimation Accumulated expected score (for each person and each item) = Accumulated raw score (for each person and each item).
Weight Selection for Tables 23 and 24: On the output tables menu, these are the options for persons and/or items. When IWEIGHT= or PWEIGHT= are used in estimation, reports can be adjusted to reflect those weights or not. Weights of zero are useful for pilot items, variant items or persons with unusual characteristics. These can be reported exclusively or excluded from reports.
(1) all items or persons are reported, with their weights (the standard). Tables 23 and 24 are computed as though all weights are 1.
(2) items or persons with a weight of 0 are excluded from the reporting. Tables 23 and 24 are computed as though all weights are 1, but zero weights are omitted.
(3) only items or persons with a weight of 0 are reported. Tables 23 and 24 are computed only from items or persons with a weight of 0.
(4) all items or persons are reported as though they have a weight of 1.
Example 1: MCQ items are scored 01. CR items are scored 00.51. How can we combine them in one Winsteps analysis.
Approach A (recommended). Double the scores of the CR items to 012, and then IWEIGHT= them by 0.5.
Approach B (not recommended). Double the scores of the MCQ items to 0(1)2, and double the scores of the CR items to 012. IWEIGHT= them all by 0.5. This gives the MCQ items a rating scale in which the middle category is not observed, making their ICCs steeper.
Example 2: What is the cutscore in a weighted analysis corresponding to a cutscore in an unweighted analysis?
Here is an approach:
1.In the unweighted analysis, identify the logit value of the cutscore. Save the person measures to Excel.
2.In the weighted analysis, save the person measures to Excel.
3.Crossplot the weighted person measures (yaxis) against the unweighted person measures (xaxis)
4.Use the Excel "trend line" function to obtain a reasonable curve through the personmeasure points.
5.Identify the value on the yaxis (weighted cutscore measure) corresponding to the value on the xaxis of the unweighted cutscore measure.
Help for Winsteps Rasch Measurement Software: www.winsteps.com. Author: John Michael Linacre
The Languages of Love: draw a map of yours!
For more information, contact info@winsteps.com or use the Contact Form
Facets Rasch measurement software.
Buy for $149. & site licenses.
Freeware student/evaluation download Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download 

Stateoftheart : singleuser and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied Rasch, Winsteps, Facets online Tutorials 

Forum  Rasch Measurement Forum to discuss any Raschrelated topic 
Click here to add your email address to the Winsteps and Facets email list for notifications.
Click here to ask a question or make a suggestion about Winsteps and Facets software.
Coming Winsteps & Facets Events  

May 22  24, 2018, Tues.Thur.  EALTA 2018 preconference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank WeissMotz), https://ealta2018.testdaf.de 
May 25  June 22, 2018, Fri.Fri.  Online 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.  Online workshop: Practical Rasch Measurement  Further Topics (E. Smith, Winsteps), www.statistics.com 
July 25  July 27, 2018, Wed.Fri.  PacificRim Objective Measurement Symposium (PROMS), (Preconference workshops July 2324, 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.  Online workshop: ManyFacet Rasch Measurement (E. Smith, Facets), www.statistics.com 
Oct. 12  Nov. 9, 2018, Fri.Fri.  Online workshop: Practical Rasch Measurement  Core Topics (E. Smith, Winsteps), www.statistics.com 
Our current URL is www.winsteps.com
Winsteps^{®} is a registered trademark
John "Mike" L.'s Wellness Report:
I'm 72, take no medications and, March 2018, my doctor is annoyed with me  I'm too healthy! According to Wikipedia, the human body requires about 30 minerals, maybe more. There are 60 naturallyoccurring minerals in the liquid Mineral Supplement which I take daily. 