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Title: A multiple correspondence analysis for aggregated symbolic data Authors:  Junji Nakano - Chuo University (Japan) [presenting]
Nobuo Shimizu - The Institute of Statistical Mathematics (Japan)
Yoshikazu Yamamoto - Tokushima Bunri University (Japan)
Abstract: When we have a huge amount of data, we sometimes are interested in comparing meaningful groups of data, not individual observations. Aggregated symbolic data (ASD) expresses a group of observations that have continuous and categorical variables by using up to second moments of variables. ASD for a group of data is equivalent to the set of means, variances, and correlations for continuous variables, Burt matrix for categorical variables, and means of a continuous variable against one value of a categorical variable. As ASD with many categorical variables is still complicated, it is preferable to have simple measures of location and dispersion for a categorical variable, and a measure of the correlation between two categorical and/or continuous variables. We propose such measures by extending multiple correspondence analysis to ASD. They are compared with other measures, for example, correlation measures based on the polychoric correlation coefficient.