# RMT 23:1 Notes and Quotes

## Georg Rasch, Factor Analysis and Scales

[Georg] Rasch was strongly against exploratory factor analysis, for two reasons. Not only because it was based on unrealistic assumptions like linearity and normality, but also because it was exploratory. He therefore always stressed that Rasch analysis is confirmatory. That it does require a theory of the construct and that the purpose of the analysis was both to check the theory and to check the items.

And Rasch never talked about interval scales. To Rasch, the constructs that we measure by Rasch models are constructs on ratio scales with absolute zeros and arbitrary units. Taking the logarithm of a ratio scale measure ["for practical purposes", Rasch, 1980, p.80] creates something similar to an interval scale since the arbitrary unit of the ratio scale is transformed into an arbitrary origin of the logit scale. An arbitrary unit on the logit scale corresponds to an arbitrary power transformation on the ratio scale, which is rarely taken to be part of the definition of ratio scales.

Svend Kreiner

 Item Characteristic Curves: Model and Empirical. Figure 3 in Rashid et. al (2008) WSEAS Transactions on Advance in Engineering Education, 8, 5, 591-602

## Infit Mean-squares: Mean ± 2 S.D.

"There are no hard-and-fast rules for setting upper- and lower-control limits for the infit statistics (i.e., infit mean-square index). In general, as Pollitt and Hutchinson (1987) suggest, any individual infit mean-square value needs to be interpreted against the mean and standard deviation of the set of infit-mean square values for the facet concerned. Using these criteria, a value lower than the mean minus twice the standard deviation would indicate too little variation, lack of independence, or overfit. A value greater than the mean plus twice the standard deviation would indicate too much unpredictability, or misfit." (Park, 2004)

Comment: This advice accords with an investigation into "Do the data fit the model usefully". The mean-squares are geometric with a range of 0-1-∞, which suggests that the computation of mean and standard deviation should be done using loge(mean-squares). In general, overfit (low mean-square) is generally a much smaller threat to the validity of the measures than excessive unpredictability (high mean-square).

Park, T. (2004) An investigation of an ESL placement test using Many-Facet Rasch Measurement. Teachers College, Columbia University Working Papers in TESOL and Applied Linguistics, 4, 1

journals.tc-library.org/index.php/tesol/article/view/41/48

Pollitt, A., & Hutchinson, C. (1987). Calibrated graded assessment: Rasch partial credit analysis of performance in writing. Language Testing, 4, 72-92.

Various (2009) Notes and Quotes, Rasch Measurement Transactions, 2009, 23:1, 1197

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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