Correspondence Analysis Results - Options Tab

Select the Options tab of the Correspondence Analysis Results dialog box to access the options described here.

Number of dimensions. Use the options in the Number of dimensions group box to determine the number of dimensions for which to compute row and column coordinates (for spreadsheets and plots of points options available on the Quick and Advanced tabs).

Number of dimensions. If you select the Number of dimensions option button, you can enter a fixed number of dimensions in the field adjacent to the option.

Cumulative contribution to inertia. If you select the Cumulative contribution to inertia option button, STATISTICA determines the minimum number of dimensions necessary so that the cumulative percent of total inertia is equal to or exceeds the respective percentage value, specified in the field below this option.

Note: The maximum number of eigenvalues that can be extracted from a two-way table is equal to the minimum of the number of columns or rows, minus 1. If you choose to extract the maximum number of dimensions that can be extracted, then you can reproduce exactly all information contained in the input table (see Computational details for details concerning the overall "model" equation).

Standardization of coordinates. Use the Standardization of coordinates group box to select the method of standardization for the coordinates. As described in the Introductory Overview, the computation and interpretation of the coordinates for the row and column points depend on the method of standardization that is selected. Following the notation used in Greenacre (1984), correspondence analysis is based on the generalized singular value decomposition of the table of relative frequencies (relative to the total sum of all values in the table); let that table of relative frequencies be denoted as matrix P. Further, let matrices Dr and Dc be diagonal matrices, with diagonal elements equal to the row totals and column totals of P, respectively. STATISTICA computes the generalized singular value decomposition of P:

P = A DuB'

so that

A inverse(Dr)A = B' inverse(Dc)B = I

where A is the matrix of the left-side generalized singular vectors, B is the matrix of the right-side generalized singular vectors, Du is a diagonal matrix with the diagonal elements equal to the generalized singular values (reported via the Eigenvalues button, on the Advanced tab), and I stands for the identity matrix (a diagonal matrix with 1's in the diagonal). The standardization options available in the Standardization of coordinates group box can then be summarized as follows:

Row & column profiles. Select the Row & column profiles option button to compute the row coordinates based on the row profile matrix R = inverse(Dr)P, and the column coordinates are computed based on the column profile matrix computed analogously. Specifically, the row coordinates are computed as inverse(Dr)ADu, and the column coordinates as inverse(Dc)BDu. This option is appropriate when you are interested in interpreting both the distances between row points and the distances between column points (the distances in both coordinate systems for row points and column points are Chi-square distances). However, note that, as discussed in the Introductory Overview, distances between column and row points are not meaningful.

Canonical standardization. Select the Canonical standardization option button to compute the row coordinates as inverse(Dr)ADu½, and the column coordinates as inverse(Dc)BDu½. For details concerning this standardization, see Gifi (1981).

Row profiles (interpret row dist.). Select the Row profiles (interpret row dist.) option button to compute the row coordinates based on the row profile matrix R = inverse(Dr)P. Specifically, the (principal) row coordinates are computed as inverse(Dr)ADu, and the standard column coordinates as inverse(Dc)B. This option is appropriate when you are interested in interpreting the distances between row points; the column coordinates should not be interpreted.

Column profiles (interpret col. dist.). Select the Column profiles (interpret col. dist.) option button to compute the column coordinates based on the column profile matrix. Specifically, the (principal) column coordinates are computed as inverse(Dc)BDu, and the standard row coordinates as inverse(Dr)A. This option is appropriate when you are interested in interpreting the distances between column points; the row coordinates should not be interpreted.

Note: computation of quality and inertia. Note that the choice of the standardization method does not affect the computation of the quality and inertia values reported in the spreadsheet that is displayed when you click the Row and column coordinates button (Advanced tab). Those values are always computed based on the Row and column profiles (see above)standardization.