Factor Analysis and Rasch Analysis

Factor analysis is confused by ordinal variables and highly correlated factors. Rasch analysis excels at constructing linearity out of ordinality and at aiding the identification of the core construct inside a fog of collinearity. This is the message of Structural Equation Modeling (3:1, 1996, Randall E. Schumacker, Ed.), a journal issue with 4 articles on the connections between Rasch and Factor analysis.

"Comparing Rasch Measurement and Factor Analysis" (Benjamin D. Wright, pp. 3-24) uses an example based on a 13 item "Strength of Principal Leadership" protocol to contrast the mathematical basis and analytic implications of the two techniques. Wright notes that both misfit to the Rasch model (dimensionality) and the extremities of the unidimensional variable are reported as minor factors by principal component analysis. Further factors are produced by accidental fluctuations in measurement error variance. When a factor cannot be confirmed or established by Rasch analysis, its existence is doubtful.[See also Comparing factor analysis and Rasch measurement, Wright B.D.]

"A Comparison of Methods for Determining Dimensionality in Rasch Measurement" (Richard M. Smith, pp. 25-40) uses simulation to investigate which technique is better at discovering dimensionality. The conclusions are simple. When the data are dominated equally by uncorrelated factors, use factor analysis. When they are dominated by highly correlated factors, use Rasch. If one factor dominates, use Rasch. This confirms Thurstone's view of factor analysis as an exploratory device for the analyst completely at a loss as to how to make sense of the data. Once a factor has been identified, however, separate its items out of the test and use Rasch analysis to analyze them further. For a complex example, see Goekoop and Zwinderman (1994).

"Finding Two Dimensions in MMPI-2 Depression" (Chih-Hung Chang, pp. 41-49) is a case study demonstrating that Rasch and Factor analysis produce similar results (mental depression and physical depression dimensions in the MMPI-2 depression scale), but that Rasch results are simpler to interpret, more stable and more informative. Factor analysis identifies closeness to the underlying variable, but not location on it. Rasch, in contrast, provides item and person location on the variable, facilitating the development of a construct theory.

"Dimensional Analyses of Complex Data" (Kathy E. Green, pp. 50- 61) notes that a vague factor structure can result in Rasch and Factor analysis suggesting different factors. [But isn't that the fun of factor analysis? If each of us use a different variance partitioning, rotation and obliqueness, then each of us can produce a different factor structure - our own personal existential "truth"!] Using several empirical data sets, Green illustrates the necessity of building from the known into the unknown. A core of items on one factor (variable) is identified. Other items are added, if possible. Then these are put to one side and another core identified. A successful core is one that can be summarized in a few words and whose items form a comprehendible ordered progression along a latent variable.

Goekoop J.G., Zwinderman A.H. (1994) Multi-dimensional hierarchic ordering of psychopathology. Acta Psychiatrica Scandinavica 90: 399-404.

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

Factor analysis and Rasch analysis. Schumacker RE, Linacre JM. … Rasch Measurement Transactions, 1996, 9:4 p.470

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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