COMPARING FACTOR ANALYSIS AND RASCH MEASUREMENT | ||
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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 | ![]() |
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Estimated by Minimizing | ![]() |
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Anchored at | ![]() |
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Error Model | ![]() |
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Item Estimate | vi regression of factor score un on item i | Di linear calibration of item i on variable |
Item Estimate Error | ![]() |
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Person Estimate | un score predicted for person n on factor | Bn linear measure of person n on variable |
Person Estimate Error | ![]() |
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Residual Statistics | ![]() |
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Misfits | ![]() |
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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 Publications | ||||
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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 |
Forum | Rasch Measurement Forum to discuss any Rasch-related topic |
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Coming Rasch-related Events | |
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June 23 - July 21, 2023, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
Aug. 11 - Sept. 8, 2023, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
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