# Computation of OUTFIT and INFIT Statistics

 Reproduced from Rating Scale Analysis (Wright BD & Masters GN, Chicago, MESA Press, 1982, p.100) with permission

Page 100 of Rating Scale Analysis (Wright and Masters 1982), which summarizes the calculation of outfit and infit statistics, is displayed in a revised form adjacent.

The Rasch residuals are the differences between the observations and their expected values according to the Rasch model. Outfit is based on a sum of squared standardized residuals. Standardized residuals are modeled to approximate a unit normal distribution. Their sum of squares approximates a χ² distribution. Dividing this sum by its degrees of freedom yields a mean-square value, OUTFIT MEANSQ, with expectation 1.0 and range 0 to infinity. Values larger than 1.0 indicate unmodeled noise. Values are on a ratio scale, so that 1.2 indicates 20% excess noise. Values less than 1.0 indicate overfit of the data to the model, i.e., the observations are too predictable.

A Wilson-Hilferty transformation standardizes the mean-square into its OUTFIT ZSTD value. This approximates a unit-normal distribution corresponding to a t-statistic with infinite degrees of freedom. It is a test of the hypothesis "these data fit the Rasch model (exactly)."

Infit is an information-weighted form of outfit. The weighting reduces the influence of less informative, low variance, off-target responses. It is also computed in INFIT MEANSQ and INFIT ZSTD forms.

This computation is the same for persons and items with appropriate adjustment of subscripts and summations.

Note: Practical considerations in the computation of the ZSTD values.
1. the lower limit of the degrees of freedom of the mean-square statistic is set at 1. qi is not allowed to be more than √2 for both
2. the contribution to the model variance of the OUTFIT MEANSQ by one observation is not allowed to overwhelm the contributions of the other observations. W²ni is not allowed to be less than 0.00001

Computation of OUTFIT and INFIT Statistics. Wright BD, Masters GN. … Rasch Measurement Transactions, 1990, 3:4 p.84-5

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.orgplease 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: Write here: Your email address (if you want us to reply):

 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
May 17 - June 21, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024
June 21 - July 19, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 5 - Aug. 6, 2024, Fri.-Fri. 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

The URL of this page is www.rasch.org/rmt/rmt34e.htm

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