COMPARING FACTOR ANALYSIS AND RASCH MEASUREMENT
ASPECT	FACTOR ANALYSIS	RASCH MEASUREMENT
Motive	summarize data	construct measurement
Input Model	"linearities"	stochastic events
Missing Data	loses rows or columns, biases factors	routinely accommodated, no data lost
Co-mensuration	norm-standardized into "linearities"	criterion-classified into ordered categories xni = 0,1,2,3,,,K
Method	principal components (or common factor)	latent trait
Model
Estimated by Minimizing
Anchored at
Error Model
Item Estimate	vi regression of factor score un on item i	Di linear calibration of item i on variable
Item Estimate Error
Person Estimate	un score predicted for person n on factor	Bn linear measure of person n on variable
Person Estimate Error
Residual Statistics
Misfits
To Seek Next Variable	subtract unvi from all zni for next data maximizes residual noise	select only xni of misfitting items minimizes residual noise

Benjamin D. Wright

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

Comparing factor analysis and Rasch measurement Wright BD. … Rasch Measurement Transactions, 1994, 8:1 p.350

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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