The family of hierarchical classes models is a distinctive collection of di
rect two-sided clustering models for two-way two-mode binary data. In the a
ssociated data analysis, a data matrix D is approximated by a binary matrix
M that can be represented by a hierarchical classes model of a prespecifie
d rank k. In this procedure, a least-squares loss function in terms of disc
repancies between D and R I is minimized. The present paper describes the o
riginal hierarchical classes algorithm proposed by De Boeck and Rosenberg (
1988), which is based on an alternating greedy heuristic, and proposes a ne
w algorithm, based on an alternating branch-and-bound procedure. An extensi
ve simulation study is reported in which both algorithms are evaluated and
compared according to goodness-of-fit to the data and goodness-of-recovery
of the underlying true structure. Furthermore, three heuristics for selecti
ng models of different ranks for a given D are presented and compared. The
simulation results show that the new algorithm yields models with slightly
higher goodness-of-fit and goodness-of-recovery values.