Next-basket recommendation considers the problem of recommending a set of items into the next basket that users will purchase as a whole. In this paper, we develop a novel mixed model with preferences, popularities and transitions (M2) for the next-basket recommendation. This method models three important factors in next-basket generation process: 1) users' general preferences, 2) items' global popularities and 3) transition patterns among items. Unlike existing recurrent neural network-based approaches, M2 does not use the complicated networks to model the transitions among items, or generate embeddings for users. Instead, it has a simple encoder-decoder based approach (ed-Trans) to better model the transition patterns among items. We compared M2 with different combinations of the factors with 5 state-of-the-art next-basket recommendation methods on 4 public benchmark datasets in recommending the first, second and third next basket. Our experimental results demonstrate that M2 significantly outperforms the state-of-the-art methods on all the datasets in all the tasks, with an improvement of up to 22.1%. In addition, our ablation study demonstrates that the ed-Trans is more effective than recurrent neural networks in terms of the recommendation performance. We also have a thorough discussion on various experimental protocols and evaluation metrics for next-basket recommendation evaluation.