Partitioning Fit and Loss
The loss of each set is partitioned by the nonlinear canonical correlation analysis in several ways. The fit table presents the multiple fit, single fit, and single loss tables produced by the nonlinear canonical correlation analysis for the survey example. Note that multiple fit minus single fit equals single loss.
Single loss indicates the loss resulting from restricting variables to one set of quantifications (that is, single nominal, ordinal, or nominal). If single loss is large, it is better to treat the variables as multiple nominal. In this example, however, single fit and multiple fit are almost equal, which means that the multiple coordinates are almost on a straight line in the direction given by the weights.
Multiple fit equals the variance of the multiple category coordinates for each variable. These measures are analogous to the discrimination measures that are found in homogeneity analysis. You can examine the multiple fit table to see which variables discriminate best. For example, look at the multiple fit table for Marital status and Newspaper read most often. The fit values, summed across the two dimensions, are 1.122 for Marital status and 0.911 for Newspaper read most often. This information tells us that a person's marital status provides greater discriminatory power than the newspaper they subscribe to.
Single fit corresponds to the squared weight for each variable and equals the variance of the single category coordinates. As a result, the weights equal the standard deviations of the single category coordinates. By examining how the single fit is broken down across dimensions, we see that the variable Newspaper read most often discriminates mainly on the first dimension, and we see that the variable Marital status discriminates almost totally on the second dimension. In other words, the categories of Newspaper read most often are further apart in the first dimension than in the second, whereas the pattern is reversed for Marital status. In contrast, Age in years discriminates in both the first and second dimensions; thus, the spread of the categories is equal along both dimensions.