Characterization of long-term activity-dependent plasticity from behaviorally driven spiking activity is important for understanding the underlying mechanisms of learning and memory. In this letter, we present a computational framework for quantifying spike-timing-dependent plasticity (STDP) during behavior by identifying a functional plasticity rule solely from spiking activity. First, we formulate a flexible point-process spiking neuron model structure with STDP, which includes functions that characterize the stationary and plastic properties of the neuron. The STDP model includes a novel function for prolonged plasticity induction, as well as a more typical function for synaptic weight change based on the relative timing of input-output spike pairs. Consideration for system stability is incorporated with weight-dependent synaptic modification. Next, we formalize an estimation technique using a generalized multilinear model (GMLM) structure with basis function expansion. The weight-dependent synaptic modification adds a nonlinearity to the model, which is addressed with an iterative unconstrained optimization approach. Finally, we demonstrate successful model estimation on simulated spiking data and show that all model functions can be estimated accurately with this method across a variety of simulation parameters, such as number of inputs, output firing rate, input firing type, and simulation time. Since this approach requires only naturally generated spikes, it can be readily applied to behaving animal studies to characterize the underlying mechanisms of learning and memory.