Empirical data-based modeling of teaching material sharing network dynamics

Teaching material sharing networks (TMSN) may enrich teachers teaching capacity and quality through sharing. To effectively manage a network and its evolution, managers have to characterize members´ behaviors such as joining/leaving the network (membership) and uploading/downloading teaching materials (sharing) and network state dynamics of membership, teaching material (TM) quantity and quality. The challenge presented in this paper is to design a methodology for modeling individual behaviors and network dynamics to predict network evolution based on empirical data of the network. SCTNet, a TMSN among elementary school teachers, serves as an exemplary network for designing the modeling methodology. Novelty of the design has three folds. i) Probabilistic individual behaviors are modeled to capture the individual difference. In particular, the features of probabilities with respect to states from data are slow start, fast growth, and saturation, thus the Bass diffusion model is adopted to model how the probabilities are affected by network states ii) How network states evolve over time with respect to the current states and individual behavior probabilities is then described by a set of Bass-Model embedded difference equations. iii) Because of limited empirical data for modeling, a Quasi-bootstrap based nonlinear least square (NLS) method is used to estimate Bass model parameters of the behavior probabilities along with the network evolution. User behaviors and network dynamics thus obtained were validated via an agent-based simulation (ABS), and the results observe that the accuracy of membership evolution reproduced by ABS matches the empirical data of SCTNet by more than 95%. This proven modeling accuracy shed the light for a better TMSN network management.