Peaks and pitfalls: Unwrapping four overlooked problems in multilevel modeling of cyclic trends and their circular solutions

Multilevel cosinor models can be used to study individual differences in circadian rhythms in intensive longitudinal data (ILD) obtained with experience sampling or passive sensing throughout the day. This allows examining how individuals differ with respect to their overall level, strength of trend, and peak timings, and how these relate to each other and other covariates. However, current estimation methods in psychology suffer from critical but overlooked flaws. Specifically, standard approaches cannot properly test for a cycle's absence. We demonstrate with empirical data that a majority of individuals may not have a cycle at all. Additionally, and more critically, these techniques ignore the circular nature of peak timing defined on a 24-hour clock. This oversight leads to inaccurate peak time estimates (off by many hours) with vastly inflated uncertainty, both individually (level-1) and on average (level-2). The severity of these issues hinges on the clock time the researcher assumes a cycle starts. Furthermore, conventional correlation measures involving peak timing become uninterpretable, as their sign, strength, and significance are dependent on the same arbitrary decision. To resolve these pitfalls, we integrate methods from circular statistics within a robust Bayesian framework, allowing researchers to assess whether or not cycles are present, obtain accurate peak estimates, and utilize proper circular-linear correlation measures. Using empirical affective and heart rate data, we demonstrate the practical severity of these issues. We conclude with a call for the behavioral sciences to integrate well-established methods from other fields and propose a foundation for future research involving multimodal data.