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.


Please help with Standard Dataset 4: Andrich Rating Scale Model



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

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