Current quality control methods for crowdsourcing largely account for variations in worker responses to items by interactions between item difficulty and worker expertise. Few have taken into account the semantic relationships that can exist between the response label categories. When the number of the label categories is large, these relationships are naturally indicative of how crowd-workers respond to items, with expert workers tending to respond with more semantically related categories to the categories of true labels, and with difficult items tending to see greater spread in the responded labels. Based on these observations, we propose a new statistical model which contains a latent real-valued matrix for capturing the relatedness of response categories alongside variables for worker expertise, item difficulty and item true labels. The model can be easily extended to incorporate prior knowledge about the semantic relationships between response labels in the form of a hierarchy over them. Experiments show that compared with numerous state-of-the-art baselines, our model (both with and without the prior knowledge) yields superior true label prediction performance on four new crowdsourcing datasets featuring large sets of label categories.