Aspect-based opinion mining is widely applied to review data to aggregate or summarize opinions of a product, and the current state-of-the-art is achieved with Latent Dirichlet Allocation (LDA)-based model. Although social media data like tweets are laden with opinions, their "dirty" nature (as natural language) has discouraged researchers from applying LDA-based opinion model for product review mining. Tweets are often informal, unstructured and lacking labeled data such as categories and ratings, making it challenging for product opinion mining. In this paper, we propose an LDA-based opinion model named Twitter Opinion Topic Model (TOTM) for opinion mining and sentiment analysis. TOTM leverages hashtags, mentions, emoticons and strong sentiment words that are present in tweets in its discovery process. It improves opinion prediction by modeling the target-opinion interaction directly, thus discovering target specific opinion words, neglected in existing approaches. Moreover, we propose a new formulation of incorporating sentiment prior information into a topic model, by utilizing an existing public sentiment lexicon. This is novel in that it learns and updates with the data. We conduct experiments on 9 million tweets on electronic products, and demonstrate the improved performance of TOTM in both quantitative evaluations and qualitative analysis. We show that aspect-based opinion analysis on massive volume of tweets provides useful opinions on products.