"I would like to analyze the underlying structure of a specific
outcome instrument. What should I do first, a Rasch analysis or a
factor analysis, or do I need to analyze my data both ways?"
Rasch analysis constructs an interval variable from the dominant dimension (factor) in the data. This dominant dimension may be a hybrid, e.g., if a test has both reading and math items, then the dominant factor will reflect a composite reading-math competency. Lesser dimensions are reported as misfit. This off-dimensional behavior can be investigated by a factor analysis of residuals (Principal Components Analysis, PCA, of residuals) of those parts of the observations not explained by the Rasch dimension. That would separate reading and math items (RMT 10:3 p. 509).
Leaping first into a factor analysis of the original observations
is prone to misleading results.
(a) Since observations are non-linear, they can generate illusory factors.
(b) Factor analysis usually reports items clustering at different performance levels as different factors (RMT 8:1 p. 347). There is no way of knowing from factor analysis alone whether each factor is a dimension or a slice of a shared dimension.
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
Rasch Analysis First or Factor Analysis First? Linacre J.M. Rasch Measurement Transactions, 1998, 11:4 p. 603.
|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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