Table 23.2, 23.12, ... Item 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 item 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 23.0 Variance components scree plot for items
Table 23.1, 23.11 Principal components plots of item loadings
Table 23.2, 23.12 Item Principal components analysis/contrast of residuals
Table 23.3, 23.13 Item contrast by persons
Table 23.4, 23.14 Item contrast loadings sorted by measure
Table 23.5, 23.15 Item contrast loadings sorted by entry number
Table 23.99 Largest residual correlations for items
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 correlations based on residuals or their transformations. Letters "E", "b", etc. relate items to their unstandardized "raw" loadings on the first contrast. In this Table, Bladder and Bowel contrast with Dressing. Since Bladder and Bowel 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 10.1 etc.
The letters under "ENTRY NUMBER" refer to the plots in Table 23.2
The "cluster number" indicates a statistical clustering of the loadings (useful for splitting these items into unidimensional subtests). The clusters are obtained by doing a cluster-analysis of the loadings. The Fisher-linearized loadings are assigned to three (or less) clusters based on the centroids of the clusters.
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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 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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|Jan. 5 - Feb. 2, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|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. www.ieia.com.mx|
|April 10-12, 2018, Tues.-Thurs.||Rasch Conference: IOMW, New York, NY, www.iomw.org|
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|May 22 - 24, 2018, Tues.-Thur.||EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 27 - 29, 2018, Wed.-Fri.||Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org|
|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|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" www.promsociety.org|
|Aug. 10 - Sept. 7, 2018, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
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