User manual SPSS CATEGORIES 11.0

[. . . ] Heiser SPSS Inc. For more information about SPSS® software products, please visit our Web site at http://www. spss. com or contact SPSS Inc. 233 South Wacker Drive, 11th Floor Chicago, IL 60606-6412 Tel: (312) 651-3000 Fax: (312) 651-3668 SPSS is a registered trademark and the other product names are the trademarks of SPSS Inc. No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c)(1)(ii) of The Rights in Technical Data and Computer Software clause at 52. 227-7013. [. . . ] The fact that the first two singular values are very different is reflected in the small correlation of 0. 02 between the two dimensions. Figure 11. 17 and Figure 11. 18 show the confidence statistics for the row and column scores. The standard deviations for the rows are quite small, so you can conclude that the correspondence analysis has obtained an overall stable solution. The standard deviations for the column scores are much larger due to the row principal normalization. If you look at the correlations between the dimensions for the scores, you see that the correlations are small for the row scores and the column scores with one exception. However, the correlations for the column scores can be inflated by using column principal normalization. Figure 11. 17 Confidence statistics for row scores Standard Deviation in Dimension Staff Group Sr Managers Jr Managers Sr Employees Jr Employees Secretaries 1 . 321 . 248 . 102 . 081 . 094 2 . 316 . 225 . 050 . 056 . 070 Correlation 1-2 . 101 . 067 . 046 . 350 -. 184 Figure 11. 18 Confidence statistics for column scores Standard Deviation in Dimension Correlation 1-2 . 442 . 861 1. 044 1. 061 . 617 . 054 . 016 -. 250 Smoking None Light Medium Heavy 1 . 138 . 534 . 328 . 682 2 168 Chapter 11 Normalization Normalization is used to distribute the inertia over the row scores and column scores. Some aspects of the correspondence analysis solution, such as the singular values, the inertia per dimension, and the contributions, do not change under the various normalizations. The three most common include spreading the inertia over the row scores only, spreading the inertia over the column scores only, or spreading the inertia symmetrically over both the row scores and the column scores. The normalization used in this example is called row principal normalization. In row principal normalization, the Euclidean distances between the row points approximate chi-square distances between the rows of the correspondence table. The column scores are standardized to have a weighted sum of squared distances to the centroid of 1. Since this method maximizes the distances between row categories, you should use row principal normalization if you are primarily interested in seeing how categories of the row variable differ from each other. On the other hand, you might want to approximate the chi-square distances between the columns of the correspondence table. In that case, the column scores should be the weighted average of the row scores. The row scores are standardized to have a weighted sum of squared distances to the centroid of 1. This method maximizes the distances between column categories and should be used if you are primarily concerned with how categories of the column variable differ from each other. This normalization spreads inertia symmetrically over the rows and over the columns. The inertia is divided equally over the row scores and the column scores. Note that neither the distances between the row points nor the distances between the column points are approximations of chisquare distances in this case. Use this method if you are primarily interested in the differences or similarities between the two variables. A fourth option is called principal normalization, in which the inertia is spread twice in the solution, once over the row scores and once over the column scores. You should use this method if you are interested in the distances between the row points and the distances between the column points separately, but not in how the row and column points are related to each other. [. . . ] Graphical display of interaction in multiway contingency tables by use of homogeneity analysis. Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables. 1994, Elements of dual scaling: An introduction to practical data analysis. Dividing the indivisible: Using smple symmetry to partition variance explained. [. . . ]