Conventional factor analysis vs. Rasch residual factor analysis

  Conventional Factor Analysis (SPSS, SAS) Rasch Residual Factor Analysis (Winsteps)
Data: Ordinal observations. Standardized residuals.
Motivation: To explain the data. To discover contrasting sub-structures by decomposing the residual variance.
Method: Common factor. Principal components.
Applied to: Items. Items or Persons.
Interpretation: Each common factor is one "dimension". Each principal component is a contrast between "types". Each "type" may be a "dimension".
Optimum result: One huge dimension explains everything. Small chance-sized contrasts, i.e., no residual sub-structures.
Cautionary result: Many small dimensions indicate construct chaos. A contrast explaining more variance than the measures indicates construct collision.
Cautionary action: Discard the data as invalid. Rescore observations, segment items/persons.
Rotation: Yes - to simplify factor interpretation. No - to preserve absolute contrast sizes.
Oblique: Yes - to optimize commonalities. No - to preserve contrast uniqueness.
Missing data: Listwise or pairwise deletion. This can distort factor structure. Imputed as fitting data, i.e., zero residuals. This can attenuate contrasts.

For more information,
The Impact of Rasch Item Difficulty on Confirmatory Factor Analysis , S.V. Aryadoust … Rasch Measurement Transactions, 2009, 23:2 p. 1207
Confirmatory factor analysis vs. Rasch approaches: Differences and Measurement Implications, M.T. Ewing, T. Salzberger, R.R. Sinkovics … Rasch Measurement Transactions, 2009, 23:1 p. 1194-5
Conventional factor analysis vs. Rasch residual factor analysis, Wright, B.D. … 2000, 14:2 p. 753.
Rasch Analysis First or Factor Analysis First? Linacre J.M. … 1998, 11:4 p. 603.
Factor analysis and Rasch analysis, Schumacker RE, Linacre JM. … 1996, 9:4 p.470
Too many factors in Factor Analysis? Bond TG. … 1994, 8:1 p.347
Comparing factor analysis and Rasch measurement, Wright BD. … 1994, 8:1 p.350
Factor analysis vs. Rasch analysis of items, Wright BD. … 5:1 p.134

Conventional factor analysis vs. Rasch residual factor analysis. Wright, B.D. … Rasch Measurement Transactions, 2000, 14:2 p. 753.



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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