As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the mainstream method due to their principled characterization and competitive performances. Here, we propose a novel PGM without imposing any distributional assumptions on attributes, which is superior to the existing PGMs that require attributes to be categorical or Gaussian distributed. Based on the block model of graph structure, our model incorporates the attribute by describing its effect on node popularity. To characterize the effect quantitatively, we analyze the community detectability for our model and then establish the requirements of the node popularity term. This leads to a new scheme for the crucial model selection problem in choosing and solving attributed community detection models. With the model determined, an efficient algorithm is developed to estimate the parameters and to infer the communities. The proposed method is validated from two aspects. First, the effectiveness of our algorithm is theoretically guaranteed by the detectability condition. Second, extensive experiments indicate that our method not only outperforms the competing approaches on the employed datasets, but also shows better applicability to networks with various node attributes.