ASYMPTOTIC BEHAVIOR OF AN CRITERION FOR ESTIMATION OF DIMENSIONALITY IN CORRESPONDENCE ANALYSIS

Abstract

Correspondence analysis is often used for analysis of the relevance of the category data of a two-way contingency table. The notion of dimensionality in correspondence analysis has been introduced in an analogy with canonical correlation analysis. It reveals with the dimension in which space the relationship can be contracted. A criterion for estimating the dimensionality has been proposed by Ogura and Fujikoshi (2013), by modifying a formal AIC. In this paper, first we note that the criterion is related to an estimator of the expected prediction error in least squares. Then, we study asymptotic behavior of the criterion by simulation experiments. Through simulation experiments and an application to a real data, it is shown that our criterion works well.