Applying the Bootstrap to Generate Confidence Regions in Multiple Correspondence Analysis

The bootstrap method, introduced in 1979 by Efron, promised to provide a means to solve many previously unsolved problems in statistics. Among these problems a prominent place is taken by the determination of statistical properties of complex methods for multivariate data analysis. Here we may think of multiparameter models for the exploratory analysis of multivariate data of mixed measurement level, which are usually applied in several steps (cf. Diaconis & Efron, 1983). In the last decade a large number of results on the bootstrap method have been published, most of which, however, concern univariate single parameter models. Although this attention for the relatively simple may be understood from a theoretical point of view, it is not very satisfactory for the practice of data analysis. In this paper we report on a study that may be considered as an approach from the other side. We take a complex method, i.e. multiple correspondence analysis, and try to find out what the bootstrap could contribute to data analysis. This is done mainly by Monte Carlo methods. After a short explanation of the multivariate method and the general methodology, results are reported of two Monte Carlo studies.