On Fitting a Continuous-Time Stochastic Process Model in the Bayesian Framework
Process models can be viewed as mathematical tools that allow researchers to formulate and test theories on the data-generating mechanism underlying observed data. In this chapter we highlight the advantages of this approach by proposing a multilevel, continuous-time stochastic process model to capture the dynamical homeostatic process that underlies observed intensive longitudinal data. Within the multilevel framework, we also link the dynamical processes parameters to time-varying and time-invariant covariates. However, estimating all model parameters (e.g., process model parameters and regression coefficients) simultaneously requires custom-made implementation of the parameter estimation; therefore we advocate the use of a Bayesian statistical framework for fitting these complex process models. We illustrate application to data on self-reported affective states collected in an ecological momentary assessment setting.
The research reported in this paper was sponsored by grant #48192 from the John Templeton Foundation, the National Institutes of Health (R01 HD076994, UL TR000127), and the Penn State Social Science Research Institute.
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