Analyzing mobility behavior of users is extremely useful to create or improve existing services. Several research works have been done in order to study mobility behavior of users that mainly use users' significant locations. However, these existing analysis are extremely intrusive because they require the knowledge of the frequently visited places of users, which thus makes it fairly easy to identify them. Consequently, in this paper, we present a privacy-aware methodology to analyze mobility behavior of users. We firstly propose a new metric based on the well-known Shannon entropy, called spatio-temporal entropy, to quantify the mobility level of a user during a time window. Then, we compute a sequence of spatio-temporal entropy from the location history of the user that expresses user's movements as rhythms. We secondly present how to study the effects of several groups of additional variables on the evolution of the spatio-temporal entropy of a user, such as spatio-temporal, demographic and mean of transportation variables. For this, we use Generalized Additive Models (GAMs). The results firstly show that the spatio-temporal entropy and GAMs are an ideal combination to understand mobility behavior of an individual user or a group of users. We also evaluate the prediction accuracy of a global GAM compared to individual GAMs and individual AutoRegressive Integrated Moving Average (ARIMA) models. These last results highlighted that the global GAM gives more accurate predictions of spatio-temporal entropy by checking the Mean Absolute Error (MAE). In addition, this research work opens various threads, such as the prediction of demographic data of users or the creation of personalized mobility prediction models by using movement rhythm characteristics of a user.