Stochastic and Deterministic Differential Equation Modeling: The Accuracy of Recovering Dynamic Model Parameters of Change

The analysis of change is an extensively studied and complicated topic in the social sciences. A variety of statistical methods that may conceptualize change in potentially many different ways may be used to assess change in a phenomenon over a specified time interval. Resultantly, conceptual differences in defining change will be addressed. In addition, the major advantages of utilizing continuous time differential equation models will be illustrated, and the classification criteria of such models will be discussed. Broadly speaking, differential equations may be classified according to at least five dimensions; one of these dimensions is the distinction between deterministic and stochastic models. The primary difference between these two models is whether or not random fluctuations of the process itself are explicitly accounted for in the differential equation. The accuracy of the deterministic and stochastic differential equation models in recovering simulated dynamic model parameters of change is examined over a wide variety of conditions likely to occur in practice for social science phenomena. Results are summarized in terms of practical implications and general guidelines for employing these two types of continuous time differential equation modeling techniques.