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 row and column scores and their variances are affected. Correspondence analysis has several ways to spread the inertia. 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.

Row principal. In row principal normalization, the Euclidean distances between the row points approximate chi-square distances between the rows of the correspondence table. The row scores are the weighted average of the column scores. 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.

Column principal. 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.

Symmetrical. You can also treat the rows and columns symmetrically. This normalization spreads inertia equally over the row and column scores. Note that neither the distances between the row points nor the distances between the column points are approximations of chi-square distances in this case. Use this method if you are primarily interested in the differences or similarities between the two variables. Usually, this is the preferred method to make biplots.

Principal. 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. Biplots are not appropriate for this normalization option and are therefore not available if you have specified the principal normalization method.

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