Users of parallel machines need to have a good grasp for how different communication patterns and styles affect the performance of message-passing applications. MPI Collective communications involve multiple processors, and their performance prediction is a tricky task to perform. In order to evaluate the performance of collective communications, we attempt to extend LogGP and P-LogP standard point-to-point models. Our objective is to compare these models with the empirical data, and identify the most suitable for performance characterization of collective communications. The models proposed are related with the implemented algorithms in MPICH. The experimental results performed on clusters of 16 and 64 processors connected by Infiniband and Gigabit Ethernet networks respectively, show the same trend. For any collective operation, given a number of processors and a range of message sizes, there is at least one model that predicts the performance precisely.