Person Fit Statistics: What is Their Purpose?

"The objective of person-fit measurement is to detect item-score patterns that are improbable given an IRT model or given the other patterns in a sample." (Meijer & Sitsma, 2001)

This sounds correct to the conventional statistician, but W. E. Deming's response to this line of reasoning was: "Of course we don't wish to violate specifications, but we must do better" (Neave, 1990, p.169).

Here are ways we can do better:

(i) Person-fit measurement must not only identify patterns that are improbable, but also ones that are too probable! The Rasch model predicts uncertainty. Too much certainty can indicate a constraint on the responses, perhaps the hidden imputation of "wrong" to not-reached items, or a response set on an attitude survey. Since the substantive length of a logit depends on the randomness in the data, constraints on the data artificially reduce the randomness. This makes the differences between items and persons appear greater when expressed in logits. If the constraints are limited to a subset of persons or items, then the measurement system is distorted accordingly.

(ii) Person-measurement fit statistics must flag misleading or ambiguous measures. Simply because a response string is improbable does not mean that it is misleading, and vice-versa. Meijer & Sitsma (2001) criticize residual-based fit statistics, such as OUTFIT and INFIT, because they "do not reflect the probability of ordering of the score patterns" (p.130). This is true, but is it relevant? What is needed is an indication of how much misfit disturbs the estimated measures, not the likelihood of any particular response pattern.

The Old Advice is still the Good Advice

Meijer & Sitsma (2001) end their section "Improving Measurement Practice" with this sound advice:

"Smith (1985) mentioned four actions that could be taken when an item-score pattern is classified as misfitting:
(1) report several [ability] estimates (rather than just one) for an examinee based on subtests that are in agreement with the model,
(2) modify the item-score pattern (e.g., eliminate the unreached items at the end) and re-estimate [ability],
(3) do not report the [ability] estimate and retest the examinee, or
(4) decide that the error is small enough for the impact on [ability] to be [negligible]. ...

Which of these actions is taken depends on the context in which testing takes place. The usefulness of a person-fit statistic thus also depends heavily on the application for which it is intended."

Meijer R.R., & Sijtsma K. (2001) Methodology review: evaluating person fit. Applied Psychological Measurement 25(2), 107-135

Neave H.R. (1990) The Deming Dimension. Knoxville TN: SPC Press.

Smith R.M. (1985) A comparison of Rasch person analysis and robust estimators. Educational and Psychological Measurement, 16, 149-157.

Person Fit Statistic - What is Their Purpose? Meijer R.R., Sitsma K. … Rasch Measurement Transactions, 2001, 15:2 p. 823

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
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 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,

Coming Rasch-related Events
Oct. 6 - Nov. 3, 2023, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets),
Oct. 12, 2023, Thursday 5 to 7 pm Colombian timeOn-line workshop: Deconstruyendo el concepto de validez y Discusiones sobre estimaciones de confiabilidad SICAPSI (J. Escobar, C.Pardo)
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),


The URL of this page is