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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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
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