# Correspondence Analysis in Practice by Michael Greenacre

By Michael Greenacre

Drawing at the author’s forty five years of expertise in multivariate research, **Correspondence research in perform, 3rd version, **shows how the flexible approach to correspondence research (CA) can be utilized for info visualization in a large choice of occasions. CA and its versions, subset CA, a number of CA and joint CA, translate two-way and multi-way tables into extra readable graphical varieties ― excellent for functions within the social, environmental and healthiness sciences, in addition to advertising, economics, linguistics, archaeology, and more.

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Michael Greenacre

is Professor of statistics on the Universitat Pompeu Fabra, Barcelona, Spain, the place he teaches a path, among others, on information Visualization. He has authored and co-edited 9 books and eighty magazine articles and ebook chapters, totally on correspondence research, the newest being *Visualization and Verbalization of Data* in 2015. He has given brief classes in fifteen international locations to environmental scientists, sociologists, information scientists and advertising pros, and has really expert in data in ecology and social science.

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**Example text**

SUMMARY: Chi-Square Distance and Inertia 1. The chi-square (χ2 ) statistic is an overall measure of the difference between the observed frequencies in a contingency table and the expected frequencies, calculated under a hypothesis of homogeneity of the row profiles (or of the column profiles). 2. The (total) inertia of a contingency table is the χ2 statistic divided by the total of the table. 3. Geometrically, the inertia measures how “far” the row profiles (or the column profiles) are from their average profile.

P and yj , j = 1, . . , p are two points in p-dimensional space. In principal component analysis (PCA), a method closely related to CA, the p dimensions are defined by continuous variables, often on different measurement scales. e. by replacing observations xj and yj for variable j by xj /sj and yj /sj . This operation can be thought of as using a weighted Euclidean distance with weights wj = 1/s2j , the inverse of the variances. e. the inverses of the average profile elements. Although the profiles are on the same relative frequency scale, there is still a need to compensate for different variances, similar to the situation in PCA.

Since we cannot easily observe or even imagine points in a space with more than three dimensions, it becomes necessary to reduce the dimensionality of the points. This dimension-reducing step is the crucial analytical aspect of correspondence analysis (CA) and can be performed only with a certain loss of information, but the objective is to restrict this loss to a minimum so that a maximum amount of information is retained. Contents Data set 3: Spanish National Health Survey . Comparison of age group (row) profiles .