In recent years, service-oriented IoT architectures have received a lot of attention from academia and industry. By encapsulating IoT resources into intelligent IoT services, interconnecting and collaborating these resource-constrained and capacity-evolving IoT services to facilitate IoT applications has become a widely adopted and flexible mechanism. Upon capacity-fluctuating and resource-varying edge devices, IoT services may experience QoS degradations or resource mismatches during their execution, making it difficult for IoT applications to continue and possibly inducing failures. Therefore, quantitative monitoring of IoT services at runtime has become the key to guaranteeing the robustness of IoT applications. Different monitoring mechanisms have been proposed in recent literature, but they are inadequate in formal interpretation with strong domain relevance and empirical subjectivity. Based on formal methods, such as signal temporal logic (STL), the problem of IoT service monitoring can be formulated as a temporal logic task to achieve runtime quantitative monitoring. However, STL and its extensions suffer from issues of non-differentiability, loss of soundness, and inapplicability in dynamic environments. Moreover, existing works are inadequate for the monitoring of composite services, with a lack of integrity, linkage, and dynamics. To solve these problems, this study proposes a compositional signal temporal logic (CSTL) to achieve quantitative monitoring of different QoS constraints and time constraints upon intra-, inter-, and composite services. Specifically, CSTL extends an accumulative operator based on positively and negatively biased Riemann sums to emphasize the robust satisfaction of all sub-formulae over their entire time domains and to evaluate qualitative and quantitative constraint satisfaction for IoT service monitoring. Besides, CSTL extends a compositional operator based on constraint types and composite structures, as well as dynamic variables that can vary with the dynamic environment, to effectively monitor QoS variations and temporal violations of composite services. As a result, temporal and QoS constraints upon intra-, inter-, and composite services, can be specified by CSTL formulae, and formally interpreted with qualitative and quantitative satisfaction at runtime. Extensive evaluations show that the proposed CSTL performs better than baseline techniques in terms of expressiveness, applicability, and robustness.