What do Infit and Outfit, Mean-square and Standardized mean?

These are all "fit" statistics. In a Rasch context they indicate how accurately or predictably data fit the model. Dichotomous fit statistics. Polytomous fit statistics.

Infit means inlier-sensitive or information-weighted fit. This is more sensitive to the pattern of responses to items targeted on the person, and vice-versa. For example, infit reports overfit for Guttman patterns, underfit for alternative curricula or idiosyncratic clinical groups. These patterns can be hard to diagnose and remedy.

Outfit means outlier-sensitive fit. This is more sensitive to responses to items with difficulty far from a person, and vice-versa. For example, outfit reports overfit for imputed responses, underfit for lucky guesses and careless mistakes. These are usually easy to diagnose and remedy.

Mean-square fit statistics show the size of the randomness, i.e., the amount of distortion of the measurement system. 1.0 is their expected values. Values less than 1.0 indicate observations are too predictable (redundancy, data overfit the model). Values greater than 1.0 indicate unpredictability (unmodeled noise, data underfit the model). Statistically, mean-squares are chi-square statistics divided by their degrees of freedom. Mean-squares are always positive. Mean-square ranges encountered in practice have been reported at Reasonable Mean-Square Fit Values.

In general, mean-squares near 1.0 indicate little distortion of the measurement system, regardless of the standardized value. Evaluate mean-squares high above 1.0 before mean-squares much below 1.0, because the average mean-square is usually forced to be near 1.0.

Outfit problems are less of a threat to measurement than Infit ones, but are easier to manage. To evaluate the impact of any misfit, replace suspect responses with missing values and examine the resultant changes to the measures.

Standardized fit statistics (Zstd in some computer output) are t-tests of the hypothesis "Do the data fit the model (perfectly)?" These are reported as z-scores, i.e., unit normal deviates. They show the improbability of the data, i.e., its significance, if the data actually did fit the model. 0.0 are their expected values. Less than 0.0 indicates too predictable. More than 0.0 indicates lack of predictability. Standardized values are positive and negative. For the relationship between mean-squares and standardized statistics, see www.rasch.org/rmt/rmt171n.htm

Standardized fit statistics are usually obtained by converting the mean-square statistics to the normally-distributed z-standardized ones by means of the Wilson-Hilferty cube root transformation.

Anchored runs:
Anchor values may not exactly accord with the current data. To the extent that they don't, fit statistics can be misleading. Anchor values that are too central for the current data tend to make the data appear to fit too well. Anchor values that are too dispersed for the current data tend to make the data appear noisy.

John M. Linacre

What do Infit and Outfit, Mean-square and Standardized mean? Linacre JM. … 16:2 p.878

What do Infit and Outfit, Mean-square and Standardized mean? Linacre JM. … Rasch Measurement Transactions, 2002, 16:2 p.878

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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