Table 24.2, 24.12, ... Person principal components/contrast analysis of residuals

Please do not interpret this as a usual factor analysis. These plots show contrasts between opposing factors, not loadings on one factor. For more discussion, see dimensionality and contrasts.


This Table decomposes the matrix of person correlations based on residuals to identify possible other contrasts (dimensions) that may be affecting response patterns. Specify PRCOMP=S or =R or =L to obtain this Table.


Table 24.0 Variance components scree plot for persons

Table 24.1, 24.11 Principal components plots of person loadings

Table 24.2, 24.12 Person Principal components analysis/contrast of residuals

Table 24.3, 24.13 Person contrast by items

Table 24.4, 24.14 Person contrast loadings sorted by measure

Table 24.5, 24.15 Person contrast loadings sorted by entry number

Table 24.99 Largest residual correlations for persons


Prior to this first contrast, the Rasch dimension has been extracted from the data. Residuals are those parts of the observations not explained by the Rasch dimension. According to Rasch specifications, these should be random and show no structure. The contrasts show conflicting local patterns in inter-item (or inter-person) correlations based on residuals or their transformations. Letters "E", "b", etc. relate persons to their unstandardized "raw" loadings on the first contrast.


In this Table 24.3, Landman and Rossner contrast with Chazelle and Ernst. Since Landman and Rossner misfit, they load on a second dimension in the data.



The loading is that on the first PCA contrast. It is unstandardized. In the factor analysis literature, values of ±.4 or more extreme are considered substantive. To standardize the loading, divide the loadings by their root-mean-square.

The measures and mean-square statistics are the same as those reported in Table 6 etc.

The letters under "ENTRY NUMBER" refer to the plots in Table 24.2.


The "cluster number" indicates a statistical clustering of the loadings (useful for splitting these persons into two or more unidimensional sub-samples). The clusters are obtained by doing a cluster-analysis of the loadings.


To copy numbers out of this Table, use WORD to copy a rectangle of text or copy-and-paste into Excel, then "text to columns".

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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 with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind 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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Coming Rasch-related Events
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
Jan. 22-24, 2018, Mon-Wed. In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico.
April 10-12, 2018, Tues.-Thurs. Rasch Conference: IOMW, New York, NY,
April 13-17, 2018, Fri.-Tues. AERA, New York, NY,
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz),
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France.,
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps),
July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences"
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets),
Sept. 3 - 6, 2018, Mon.-Thurs. IMEKO World Congress, Belfast, Northern Ireland
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),



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