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date: 17 February 2020

Abstract and Keywords

Historically it has been easier to focus on measuring and describing differences between groups of people rather than try to describe the dynamic ways that individuals change. Dynamical systems are mathematical models that aim to describe how constructs change over time. Frequently these models are continuous time models; models that try to capture the function that underlies a set of observations. This chapter introduces the concept of a dynamical system and of continuous time models. Two methods are introduced for the fitting of continuous time models to observed data: one using the approximate discrete model for a first-order autoregressive model and the second using a method of estimating latent derivatives for a second-order autoregressive model.

Keywords: Dynamical System(s), Dynamic System(s), Continuous Time, Discrete Time, Differential Equation Model(s)(ing), Derivative Estimation, Approximate Discrete Model

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