PCA, EFA, Cluster Analysis - R Statistics

This is called from the Plots menu and performs Principal Components Analysis and Exploratory Factor Analysis using R Statistics. This confirms and complements Table 23, Item dimensionality, and Table 24, Person dimensionality. For more information, please see the R Statistics documentation for packages "psych" (scree plot, factor analysis) at cran.r-project.org/web/packages/psych/psych.pdf and "FactoMineR" (principal components analysis). cran.r-project.org/web/packages/FactoMineR/FactoMineR.pdf

 

This plot is added to Winsteps because:

1. analysts asked for a neater scree plot of the PCA contrasts in Table 23.0

2. analysts asked for confirmation of the Winsteps PCA results

3. analysts asked "If we used EFA instead of PCA, would the results be different?"

 

 

 

For most fields, see IPMATRIX=.

 

R Statistics packages are launched to perform PCA, EFA or both. A scree plot of the eigenvalues is shown.

 

 

For PCA of Standardized Residuals, the eigenvalues are shown in the R Console Window (scroll up). The observed and expected (simulated) eigenvalues confirm and augment Tables 23.0 and 24.0. In R Console window:

 

 Eigenvalues of real data

 [1] 4.62622943 2.94277448 2.29809661 1.73152686 1.63418344 1.37225606

 Eigenvalues of simulated data = expected values

 [1] 2.2386962 2.0245066 1.8715678 1.7194308 1.6214343 1.5075780 1.3897111

 

 

Cluster Analysis

R Statistics is launched with the package "pvclust" to produce a dendrogram, here for Example0, "Liking for Science". The probability of each cluster is shown in blue, red or green. Clusters wih probabilities >= 90% are boxed in red. See pvclust documentation. Notice here that the three most misfitting items are separately clustered to the left side.