A class of indexes for comparing model-based clustering solutions

Many indexes heve been introduced in the literature in order to compare two partitions determined by different clustering procedures applied to the same set of individuals (clustering procedures are considered different either when they are based on different algorithms, or when they use different data collected on the same set of individuals). Most of them are based on the number of pairs placed in the same or in different groups. Perhaps the most popular one is the Rand index. In this paper, a generalisation of some of these indexes is proposed in order to take into account the estimates of membership probabilities provided by model-based classifications. Correction for chance will also be discussed.