Opinion exchange models aim to describe the process of public opinion formation, seeking to uncover the intrinsic mechanism in social systems; however, the model results are seldom empirically justified using large-scale actual data. Online social media provide an abundance of data on opinion interaction, but the question of whether opinion models are suitable for characterizing opinion formation on social media still requires exploration. We collect a large amount of user interaction information from an actual social network, i.e., Twitter, and analyze the dynamic sentiments of users about different topics to investigate realistic opinion evolution. We find two nontrivial results from these data. First, public opinion often evolves to an ordered state in which one opinion predominates, but not to complete consensus. Second, agents are reluctant to change their opinions, and the distribution of the number of individual opinion changes follows a power law. Then, we suggest a model in which agents take external actions to express their internal opinions according to their activity. Conversely, individual actions can influence the activity and opinions of neighbors. The probability that an agent changes its opinion depends nonlinearly on the fraction of opponents who have taken an action. Simulation results show user action patterns and the evolution of public opinion in the model coincide with the empirical data. For different nonlinear parameters, the system may approach different regimes. A large decay in individual activity slows down the dynamics, but causes more ordering in the system. Opinion dynamics tries to describe the process of public opinion formation in social systems. Many opinion models have been presented that explore how the local individual behavior affects collective phenomena. However, those model results are seldom empirically justified using large-scale actual data, and whether traditional opinion models suitably describe online opinion interactions requires further exploration. We analyze users' opinions regarding a certain topic using large-scale actual data collected from a famous social network, i.e., Twitter, and discover two nontrivial results: first, consensus is difficult to achieve in a finite time and second, users seldom change their opinions, and the number of individual opinion changes decays as a power law. We present a discrete opinion model including agents' internal opinions and external actions that are determined by agents' activity. Agents' activity also evolves during the dynamics. Simulation results show our model can retrieve similar properties to those of actual data. We hope theoretical opinion models will be verified by actual data in different social systems so that they can better characterize actual social interactions. In the future, whether opinion models can predict the evolutionary trend of public opinion in actual situation will be investigated. This study will improve the applicability of research on opinion dynamics.