Computational Efficiency in Continuous (and Discrete!) Time Models – Comment on Hecht and Zitzmann. Issue 5 (3rd September 2021) - Driver, Charles
ABSTRACT: Continuous-time models generally imply a stochastic differential equation for latent processes, coupled to a measurement model. Various computational issues can arise, and there are different estimation approaches, with different trade-offs. It has been claimed that a SEM style continuous-time model can reduce run times for Bayesian estimations of continuous-time models from hours to minutes. However this claim is not true in the general case, but requires that individuals are characterized by the same covariance and means structure, and that the number of time points is not large. While such simplifications can be valuable, and indeed are in use in existing software when appropriate, they are in general quite restrictive. The hierarchical Bayesian form of ctsem was, for instance, developed precisely to estimate models where these restrictions do not hold. To try to shed some more light on these aspects, I discuss the related issues herein.