Fitting a mixture model to three-mode three-way data with categorical and continuous variables

The mixture likelihood approach to clustering is most often used with two-m ode two-way data to cluster one of the modes (e.g., the entities) into homo geneous groups on the basis of the other mode (e.g., the attributes). In th is case, the attributes can either be continuous or categorical. When the d ata set consists of a three-mode three-way array (e.g., attributes measured on entities in different situations), an analogous procedure is needed to enable the clustering of the entities (i.e., one of the modes) on the basis of both of the other modes simultaneously (i.e., the attributes measured i n different situations). In this paper, it is shown that the finite mixture approach to clustering can be extended to analyze three-mode three-way dat a where some of the attributes are continuous and some are categorical. The methodology is illustrated by clustering the genotypes in a three-way soyb ean data set where various attributes were measured on genotypes grown in s everal environments.