# Correspondence analysis

Correspondence analysis:

Correspondence analysis (CA) is an approach to representing categorical data in an Euclidean space, suitable for visual analysis. CA is often used where the data (in the form of a two-way continegency table) have many rows and/or columns and are not easy to interpret by visual inspection. The map obtained by CA helps reveal relationships within the table. CA is used in ecology, market research, and other areas.

The initial data for CA are usually in a form of a two-way contingency table .

The outcome of CA is numerical scores ascribed to values of the two variables – i.e to rows and columns. It is a common practice to derive two (or a greater number) of such sets of scores – each one representing a new dimension, orthogonal (zero-correlated) to the previous dimensions.

An essential feature of CA is that each set of scores represents both variables on the same scale. This allows to analyze interrelation not only between values of the same variable, but also between values of two different variables. This might seem somewhat paradoxical. Consider, for example, two categorical variables: cities and brands of coffee (and the cells are numbers of respondents from a random sample which purchase a particular brand and dwell in a particular city). Then, each dimension (axis) derived by CA “measures” both radically different entities – cities and brands – in the same “units”. This property of CA might help, for example, to reveal propensity of particular city inhabitants to purchase particular brand coffee – if the CA scores of the city and that brand are close on the first scale, or on the first two scales.

The extension of CA to the case of more than two variables (m-way tables) is known as multiple correspondence analysis .

Correspondence analysis is also sometimes called dual scaling, reciprocal averaging, principal components analysis of qualitative data, perceptual mapping, social space analysis, correspondence factor analysis, correspondence mapping.

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