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 23.6, 23.16 Person measures for item clusters in contrast. Cluster Measure Plot for Table 23.6.
Table 23.99 Largest residual correlations for items
Youtube video explaining Table 23
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, "bugs", "rat" and "cans" contrast with "Grow garden". Since"bugs", "rat" and "can" misfit conspicuously, 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.
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".
