Redundant Items, Overfit and Measure Bias

"One question I have is with the Rasch method's apparent failure to take account of redundant items. If the item scaling shows that all items are approximately equally spaced except for a few that are duplicates of other items (two items fall at same difficulty level), then the mapping of raw score onto Rasch ability level should take this into account, e.g., by weighting these items only .5 vs. the items that do not have duplicates being weighted 1.0." Roger Graves

What is a redundant item? For measurement purposes, we want an item that focuses on the same thing as the other items, but produces one item's worth of new information. A useful item is "as similar as possible, but as different as possible". Including the same item twice in a test is nearly always redundant. Such items do not provide two item's worth of new information, since responses to one are overly predictable from responses to the other. High inter-item dependency is typically flagged by fit statistics reporting overfit for redundant items. Dependency is also detected by response-residual analysis.

the effect of redundancy is to introduce a locally Guttman-like pattern into the data. Since Rasch measures are computed as though the data fit the model, this slightly distorts or biases the measures by locally increasing logit distances. Redundant, over-fitting or dependent items, however, rarely distort the measures enough to have any practical consequences.


The impact of redundancy in a simulated data set is shown in the Figure. The baseline consists of 100 persons taking a test of 100 dichotomous items in accordance with the Rasch model. Identical items are added to the test by copying the responses of the sample to an item at the center of the test. It is reassuring to see that large numbers of identical items have little impact on the measures. If measure bias due to item dependency is a concern, compare persons measures including and omitting those items.

Two items of the same difficulty may or may not be redundant. If responses to the two items are independent, then the items are not redundant in the measurement sense and do not distort the measures. They do increase the local precision of person measures. This is of benefit in computer-adaptive and criterion-based tests. But, if high precision is not needed, then multiple items of the same difficulty are not required, and there is pragmatic item redundancy. It may be beneficial to shorten the test, or to replace excess items of similar difficulty with items of different difficulties designed to fill gaps in the difficulty hierarchy. John Michael Linacre

Redundant Items, Overfit and Measure Bias Linacre, J.M. … Rasch Measurement Transactions, 2000, 14:3 p.755




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: 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

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

www.rasch.org welcomes your comments:

Your email address (if you want us to reply):

 

ForumRasch 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
Sept. 27-29, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
Oct. 13 - Nov. 10, 2017, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 25-27, 2017, Wed.-Fri. In-person workshop: Applying the Rasch Model hands-on introductory workshop, Melbourne, Australia (T. Bond, B&FSteps), Announcement
Dec. 6-8, 2017, Wed.-Fri. In-person workshop: Introductory Rasch Analysis using RUMM2030, Leeds, UK (M. Horton), Announcement
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
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt143a.htm

Website: www.rasch.org/rmt/contents.htm