Saturday, March 2, 2013

Correspondence Analysis - Tools comparison

The correspondence analysis (or factorial correspondence analysis) is an exploratory technique which enables to detect the salient associations in a two-way contingency table. It proposes an attractive graphical display where the rows and the columns of the table are depicted as points. Thus, we can visually identify the similarities and the differences between the rows profiles (between the columns profiles). We can also detect the associations between rows and columns.

The correspondence analysis (CA) can be viewed as an approach to decompose the chi-squared statistic associated with a two-way contingency table into orthogonal factors. In fact, because CA is a descriptive technique, it can be applied to tables even if the chi-square test of independence is not appropriate. The only restriction is that the table must contain positive or zero values, the calculating the sum of the rows and the columns is possible, the rows and columns profiles can be interpreted.

The correspondence analysis can be viewed as a factorial technique. Factors are latent variables defined from linear combinations of the rows profiles (or columns profiles). We can use the factors scores coefficients to calculate the coordinate of supplementary rows or columns.

In this tutorial, we show how to implement the CA on a realistic dataset with various tools: Tanagra 1.4.48, which incorporates new features for a better reading of the results; R software, using the "ca" and "ade4" packages; OpenStat; and SAS (PROC CORRESP). We will see - as always - that all these software produce exactly the same numerical results (fortunately!). The differences are found mainly in terms of the organization of the outputs.

Keywords: correspondence analysis, symmetric graph, R software, package ca, package ade4, openstat, sas
Tutorial: en_Tanagra_Correspondence_Analysis.pdf
References :
M. Bendixen, « A practical guide to the use of the correspondence analysis in marketing research », Marketing Research On-Line, 1 (1), pp. 16-38, 1996.
Tanagra Tutorial, "Correspondence Analysis".