Principal Components Report Options

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).

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.

Formatted Loading Matrix

Shows or hides a table of the loadings for each component. The table is sorted in order of decreasing loadings on the first principal component. Therefore, the variables are listed in the order of decreasing loadings on the first component.

Formatted Loading Matrix

Suppress Absolute Loading Value Less Than

The value that determines which loadings are unavailable in the Formatted Loading Matrix report. You can use the text box or the slider to dim the loadings whose absolute values fall below the selected value.

Dim Text

The transparency of the dimmed values in the Formatted Loading Matrix report. You can use the text box or the slider to set the degree of transparency for the dimmed loadings. The degree of transparency ranges from 0 to 1, where lower values are more transparent than higher values. For example, setting the transparency to 0 completely removes the unavailable loadings from the matrix, while the loadings are still available when you set the transparency to 1.

Squared Cosines of Variables

Shows or hides a table that contains the squared cosines of variables. The sum of the squared cosine values across principal components is equal to one for each variable. The squared cosines enable you to see how well the variables are represented by the principal components. You can also determine how many principal components are necessary to represent certain variables. This option also shows a plot of the squared cosines for the first three principal components.

Note: If the Sparse estimation method is used and the number of components selected is less than three, only the specified number of components are displayed in the plot.

Partial Contribution of Variables

Shows or hides a table that contains the partial contributions of variables. The partial contributions enable you to see the percentage that each variable contributes to each principal component. This option also shows a plot of the partial contributions for the first three principal components.

Note: If the Sparse estimation method is used and the number of components selected is less than three, only the specified number of components are displayed in the plot.

Summary Plots

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.

Tip: Select the tips of arrows in the loading plot to select the corresponding columns in the data table. Hold down Ctrl and click on an arrow tip to deselect the column.

Biplot

Shows or hides a plot that overlays the score plot and the loading plot for the specified number of components.

Biplot

Note: The score plot markers are dots and the loading plot markers are diamonds.

Scatterplot Matrix

Shows or hides a matrix of score and loading plots for a specified number of principal components. The scatterplot matrix arranges both the score plots and the loading plots in one space. The score plots have a yellow shaded background. The loading plots have a blue shaded background.

Scatterplot Matrix

Note: The loading plot matrix displayed in the Scatterplot Matrix is the transpose of the loading plot matrix that you obtain when you select the Loading Plot option.

Scree Plot

Shows or hides a graph of the eigenvalue for each component. This scree plot helps in visualizing the dimensionality of the data space.

Score Plot

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 Principal Components on Correlations Report (left-most plot).

Loading 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 Principal Components on Correlations Report (right-most plot).

Tip: Select the tips of arrows in the loading plot to select the corresponding columns in the data table. Hold down Ctrl and click on an arrow tip to deselect the column.

Score Plot with Imputation

(Not available for the Wide or Sparse estimation methods.) Imputes any missing values and creates a score plot. This option is available only if there are missing values.

3D Score Plot

(Not available for the Wide or Sparse estimation methods.) Shows or hides a 3D scatterplot of any three principal component scores. When you first invoke the command, the first three principal components are presented.

Scatterplot 3D Score Plot

Plot Source

The source of the data points in the plot. The available options are Principal Components, Rotated Principal Components, and Data Columns.

Axis Controls

The contents of each axis. If the Principal Components option or the Rotated Components option is selected, the options for the Axis Controls are principal components. If the Data Columns option is selected, the options are variables from the analysis.

Cycle Button

Cycles through all axis content possibilities.

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.

Display Options

Enables you to show or hide arrows on all plots that can display arrows. Arrows are shown if the number of variables is 1000 or fewer. If there are more than 1000 variables, the arrows are off by default.

Arrow Lines

Shows or hides arrow lines for the analysis variables in the all plots that can display arrows.

Show Supplementary Variable

(Available only if you specify a supplementary variable.) Shows or hides the arrow lines for continuous supplementary variables or label markers for categorical supplementary variables in the biplot, score plot, and loading plots.

Factor Analysis

(Not available for the Wide or Sparse estimation methods.) Performs factor analysis-style rotations of the principal components, or factor analysis. See Factor Analysis in the Consumer Research book for details.

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.

Note: Cluster Variables uses correlation matrices for all calculations, even when you select the on Covariance or on Unscaled options.

Save Principal Components

Saves the number of principal components that you specify to the data table with a formula for computing each component. The formula cannot evaluate rows with missing values.

The calculation for the principal components depends on which matrix you select for extraction of principal components:

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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.

Note: If the specified number of components exceeds the rank of the correlation matrix, then the number of components saved is set to the rank of the correlation matrix.

Save Predicteds

Saves the predicted variables with a specified number of principal components to new columns in the data table.

Save DModX

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.

Save Individual Squared Cosines

Saves the individual squared cosines to new columns in the data table.

Save Individual Partial Contributions

Saves the individual partial contributions to new columns in the data table.

Save Rotated Components

(Not available for the Wide or Sparse estimation methods.) Saves the rotated components to the data table, with a formula for computing the components. This option is available only after the Factor Analysis option is used. The formula cannot evaluate rows with missing values.

Save Principal Components with Imputation