Three-Way and Higher-Order Crossed Classifications

Abstract

Crossed classifications involving several factors are common in experiments and surveys in many substantive fields of research. Consider three factors A, B, and C with a, b, and c levels, respectively, involving a factorial arrangement. Assume that n _ijk (≥ 0) observations are taken corresponding to the (i, j, k)th cell. The model for this design is known as the unbalanced three-way crossed-classification model. This model is the same as the one considered in Chapter 5 except that now the number of observations per cell is not constant but varies from cell to cell including some cells with no data. Models of this type frequently occur in many experiments and surveys since many investigations cannot guarantee the same number of observations for each cell. In this chapter, we briefly outline the analysis of random effects model for the unbalanced three-way crossed-classification with interaction and indicate its extension to higher-order classifications.