Handling large numbers of observation units in three-way methods for the analysis of qualitative and quantitative two-way data

Recently, a number of methods have been proposed for the exploratory analysis of mixtures of qualitative and quantitative variables. In these methods for each variable an object by object similarity matrix is constructed, and these are consequently analyzed by means of three-way methods like INDSCAL, IDIOSCAL and TUCKALS-3. When the number of observation units (objects) is large, algorithms for INDSCAL, IDIOSCAL and TUCKALS-3 become. inefficient or even infeasible. The present paper offers variants of these algorithms that can handle large numbers of objects in case the similarity matrices are of rank much smaller than the number of objects, which is usually the case. In addition, it is shown that results of the three-way methods at hand are essentially based only on certain aggregate measures for the variables, like variances and covariances for numerical variables, and bivariate and marginal frequencies for nominal variables.