Model Summary

Homogeneity analysis can compute a solution for several dimensions. The maximum number of dimensions equals either the number of categories minus the number of variables with no missing data or the number of observations minus one, whichever is smaller. However, you should rarely use the maximum number of dimensions. A smaller number of dimensions is easier to interpret, and after a certain number of dimensions, the amount of additional association accounted for becomes negligible. A one-, two-, or three-dimensional solution in homogeneity analysis is very common.

Figure 1. Model summary
Model summary

Nearly all of the variance in the data is accounted for by the solution, 62.1% by the first dimension and 36.8% by the second.

The two dimensions together provide an interpretation in terms of distances. If a variable discriminates well, the objects will be close to the categories to which they belong. Ideally, objects in the same category will be close to each other (that is, they should have similar scores), and categories of different variables will be close if they belong to the same objects (that is, two objects that have similar scores for one variable should also score close to each other for the other variables in the solution).

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