Finite mixture models are frequently used to capture the underlying clustering structure of the data. They provide a model-based approach to unsupervised classification, where the mixture components are usually interpreted as clusters. However, the number of clusters is frequently unknown and should be learned from the data. When the finite mixture model is rather complex and then estimated by a composite likelihood approach, classical likelihood-based selection criteria cannot be used and should be adapted. In this paper, we compare different methods to choose such number of components when the composite likelihood is adopted. The comparison is made with particular reference to the case of ordinal data.