Several clustering approaches are adapted to binned data in order to accelerate the clustering process or to deal with data of limited precision. Bin-EM-CEM algorithms of fourteen parsimonious Gaussian mixture models are developed. Each model performs differently according to its specific feature. Without knowing any information of the data, a criterion is considered to select the best model in order to obtain a good result. In this article, BIC and ICL criteria are adapted to binned data clustering to choose the bin-EM-CEM algorithm of the right model as well as the number of clusters. By different experiments on simulated data and real data, the performance of BIC and ICL criteria in model selection for binned data clustering are studied and compared on different aspects.