MESA Note 6: Iterations and Convergence of Estimation

by John M. Linacre
MESA Research Note 6, November 1998

The Rasch model is based on the non-linear logistic function. In general, estimates for measures cannot be obtained directly, but must be obtained through a process of improving estimates until they are good enough ("converged"). The process requires performing the same computations over and over again ("iteration").

The iterative process is shorter when:

  1. The distribution of the person, item, judge, etc., measures is close to normal.
  2. The range of measures is narrow.
  3. The data are "complete".
  4. The data fit the Rasch model.
  5. The persons and items are on-target.
  6. The items are dichotomies.

In one data set with very adverse characteristics, over 600 iterations were required before meaningful estimates were obtained.

In many cases, the estimates are good enough after only a few iterations. A large number of iterations may only be needed for the final, definitive analysis.

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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
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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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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang 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
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

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