Studying if the choice of sampling interval matters for continuous-time models

What is it about?

There has been many works in the past few years that recommend the use of continuous-time models (or differential equation models) because they align more with psychological theories of a continuous underlying process but also are flexible with the sampling interval one might have. For instance, these models can rescale parameters from one interval to another (essentially, we can go from seconds to years) but should we? This is the question we address in this paper and bring caveats to the purported benefits of this model. Our findings indicate that researchers can obtain accurate results if they sample faster than the data-generating frequency (e.g., collecting data daily when the data-generating frequency was weekly). If researchers sample slower than the data-generating frequency (e.g., collecting data monthly when the data-generating frequency was weekly), then accuracy is poor unless the AR effect is very strong. We recommend that researchers use theory to determine the frequency of interest for the variable under study, and sample at that frequency or faster for best results.

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Photo by Nicholas Cappello on Unsplash

Photo by Nicholas Cappello on Unsplash

Why is it important?

Deciding on the interval at which a process should be sampled is an important but difficult task. Even though we can rescale parameters from one interval to another using continuous-time models, it is important to study if there are limitations to this flexibility and this is what our work is about. As our work shows, the rescaling of continuous-time dynamic parameters indeed works in many situations but in some it also doesn't. It is important to have a theoretical hypothesis about the strength of the process at a particular timescale before we decide to sample it.