Correspondence Analysis Model

The Model dialog box allows you to specify the number of dimensions, the distance measure, the standardization method, and the normalization method.

Dimensions in solution. Specify the number of dimensions. In general, choose as few dimensions as needed to explain most of the variation. The maximum number of dimensions depends on the number of active categories used in the analysis and on the equality constraints. The maximum number of dimensions is the smaller of:

• The number of active row categories minus the number of row categories constrained to be equal, plus the number of constrained row category sets.
• The number of active column categories minus the number of column categories constrained to be equal, plus the number of constrained column category sets.

Distance Measure. You can select the measure of distance among the rows and columns of the correspondence table. Choose one of the following alternatives:

• Chi-square. Use a weighted profile distance, where the weight is the mass of the rows or columns. This measure is required for standard correspondence analysis.
• Euclidean. Use the square root of the sum of squared differences between pairs of rows and pairs of columns.

Standardization Method. Choose one of the following alternatives:

• Row and column means are removed. Both the rows and columns are centered. This method is required for standard correspondence analysis.
• Row means are removed. Only the rows are centered.
• Column means are removed. Only the columns are centered.
• Row totals are equalized and means are removed. Before centering the rows, the row margins are equalized.
• Column totals are equalized and means are removed. Before centering the columns, the column margins are equalized.

Normalization Method. Choose one of the following alternatives:

• Symmetrical. For each dimension, the row scores are the weighted average of the column scores divided by the matching singular value, and the column scores are the weighted average of row scores divided by the matching singular value. Use this method if you want to examine the differences or similarities between the categories of the two variables.
• Principal. The distances between row points and column points are approximations of the distances in the correspondence table according to the selected distance measure. Use this method if you want to examine differences between categories of either or both variables instead of differences between the two variables.
• Row principal. The distances between row points are approximations of the distances in the correspondence table according to the selected distance measure. The row scores are the weighted average of the column scores. Use this method if you want to examine differences or similarities between categories of the row variable.
• Column principal. The distances between column points are approximations of the distances in the correspondence table according to the selected distance measure. The column scores are the weighted average of the row scores. Use this method if you want to examine differences or similarities between categories of the column variable.
• Custom. You must specify a value between –1 and 1. A value of –1 corresponds to column principal. A value of 1 corresponds to row principal. A value of 0 corresponds to symmetrical. All other values spread the inertia over both the row and column scores to varying degrees. This method is useful for making tailor-made biplots.

To Specify the Model in Correspondence Analysis

This feature requires SPSS® Statistics Professional Edition or the Categories option.

1. From the menus choose:

   Analyze > Dimension Reduction > Correspondence Analysis...

2. In the Correspondence Analysis dialog box, click Model.