Missing data

One of Ben Wright's requirements for valid measurement, derived from the work of L.L. Thurstone, is that "Missing data must not matter." Of course, missing data always matters in the sense that it lessens the amount of statistical information available for the construction and quality-control of measures. Further, if the missing data, intentionally or unintentionally, skew the measures (e.g., incorrect answers are coded as "missing responses"), then missing data definitely do matter. But generally, missing data are missing essentially at random (by design or accident) or in some way that will have minimal impact on the estimated measures (e.g., adaptive tests).


Winsteps does not require complete data in order to make estimates. One reason that Winsteps uses JMLE is that it is very flexible as regards estimable data structures. For each parameter (person, item or Rasch-Andrich threshold) there are sufficient statistics: the marginal raw scores and counts of the non-missing observations. During Winsteps estimation, the observed marginal counts and the observed and expected marginal scores are computed from the same set of non-missing observations. Missing data are skipped over in these additions. When required, Winsteps can compute an expected value for every observation (present or missing) for which the item and person estimates are known.


The basic estimation algorithm used by Winsteps is:

Improved parameter estimate = current parameter estimate

 + (observed marginal score - expected marginal score) / (modeled variance of the expected marginal score)


The observed and expected marginal scores are obtained by summing across the non-missing data. The expected score and its variance are obtained by Rasch estimation using the current set of parameter estimates, see RSA.


If data are missing, or observations are made, in such a way that measures cannot be constructed unambiguously in one frame of reference, then the message


is displayed on the Iteration screen to warn of ambiguous connection.



Missing data in Tables 23, 24: Principal Components Analysis.


For raw observations, missing data are treated as missing. Pairwise deletion is used during the correlation computations.

For residuals, missing data are treated as 0, their expected values. This attenuates the contrasts, but makes them estimable.

You can try different methods for missing data by writing an IPMATRIX= of the raw data to a file, and then using your own statistical software to analyze.



Missing data: "skipped", and "not reached"


Missing responses in a dataset do not all have the same meaning. For instance, in a time multiple-choice test. Missing responses between observed responses may mean "skipped" - the respondent decided this question was too hard. Missing responses at the end of the test can mean "not reached", because time ran out before the respondent could respond to these items.


Solution: enter two different missing data codes in the data file, for instance, "S" for skipped and "R" for not reached. Then,


when calibrating the items, we want to ignore "not reached" responses, but score skipped responses as wrong:


NEWSCORE=010  ; S is scored 0

MISSING-SCORED= -1 ; data code R is not in CODES= so it will be scored -1 = "ignore", "not administered"

IFILE= item-calibrations.txt


when we measure the persons, skipped and not reached responses are wrong:

IAFILE= item-calibrations.txt ; anchor the item difficulties at their good calibrations


NEWSCORE=0100  ; S and R are scored 0

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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 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
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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