(Not available for the Wide or Sparse estimation methods.) Enables you to create the principal components based on Correlations, Covariances, or Unscaled.
If you select the Bartlett Test option from the red triangle menu, hypothesis tests (Figure 3.6) are given for each eigenvalue (Jackson 2003).
Figure 3.5 Eigenvalues
(Not available for the Wide or Sparse estimation methods.) Shows or hides the results of the homogeneity test (appended to the Eigenvalues table). The test determines whether the eigenvalues have the same variance by calculating the Chi-square, degrees of freedom (DF), and the p-value (prob > ChiSq) for the test. See Bartlett (1937, 1954).
Figure 3.6 Bartlett Test
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For the on Correlations option, the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue. The i,jth loading is the correlation between the ith variable and the jth principal component.
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For the on Covariances option, the jth entry in the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue and divided by the standard deviation of the jth variable. The i,jth loading is the correlation between the ith variable and the jth principal component.
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For the on Unscaled option, the jth entry in the ith column of loadings is the ith eigenvector multiplied by the square root of the ith eigenvalue and divided by the standard error of the jth variable. The standard error of the jth variable is the jth diagonal entry of the sum of squares and cross products matrix divided by the number of rows (X’X/n).
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Note: When you are analyzing the unscaled data, the i,jth loading is not the correlation between the ith variable and the jth principal component.
Figure 3.7 Formatted Loading Matrix
Shows or hides the summary information produced in the default report. This summary information includes a plot of the eigenvalues, a score plot, and a loading plot. By default, the report shows the score and loading plots for the first two principal components. There are options in the report to specify which principal components to plot. See Principal Components Report.
Figure 3.8 Biplot
Figure 3.9 Scatterplot Matrix
Shows or hides a matrix of scatterplots of the scores for pairs of principal components for the specified number of components. This plot is shown in Figure 3.4 (left-most plot).
Shows or hides a matrix of two-dimensional representations of factor loadings for the specified number of components. The loading plot labels variables if the number of variables is 30 or fewer. If there are more than 30 variables, the labels are off by default. This information is shown in Figure 3.4 (right-most plot).
Figure 3.10 Scatterplot 3D Score Plot
The variables show as rays in the plot. These rays, called biplot rays, approximate the variables as a function of the principal components on the axes. If there are only two or three variables, the rays represent the variables exactly. The length of the ray corresponds to the eigenvalue or variance of the principal component.
Shows or hides the Outlier Analysis report, which enables you to detect outliers in the data through T2 and contribution statistics. For details, see Outlier Analysis.
(Not available for the Wide or Sparse estimation methods.) Performs factor analysis-style rotations of the principal components, or factor analysis. See the Factor Analysis topic.
Cluster Variables(Not available for the Wide or Sparse estimation methods.) Performs a cluster analysis on the variables by dividing the variables into non-overlapping clusters. Variable clustering provides a method for grouping similar variables into representative groups. Each cluster can then be represented by a single component or variable. The component is a linear combination of all variables in the cluster. Alternatively, the cluster can be represented by the variable identified to be the most representative member in the cluster. See the Cluster Variables topic for details.
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For the on Correlations option, the ith principal component is a linear combination of the centered and scaled observations using the entries of the ith eigenvector as coefficients.
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For the on Covariances options, the ith principal component is a linear combination of the centered observations using the entries of the ith eigenvector as coefficients.
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For the on Unscaled option, the ith principal component is a linear combination of the raw observations using the entries of the ith eigenvector as coefficients.
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Saves the observation distance to the principal components model (DModX) to a new column in the data table. Larger DModX values indicate mild to moderate outliers in the data. For more information, see DModX Calculation.
Publish Components FormulasCreates a specified number of principal component formulas and saves them as formula column scripts in the Formula Depot platform. If a Formula Depot report is not open, this option creates a Formula Depot report. See Formula Depot in the Predictive and Specialized Modeling book.
Publish DModX FormulaSaves the DModX formula based on a specified number of principal components as a formula column script in the Formula Depot platform. If a Formula Depot report is not open, this option creates a Formula Depot report. See Formula Depot in the Predictive and Specialized Modeling book.
See Local Data Filter, Redo Menus, and Save Script Menus in the Using JMP book for more information about the following options: