Modeling cyclic patterns using a two-stage hybrid Bayesian approach

Cyclical phenomena are commonly observed, particularly in intensive longitudinal data. The conventional approach to analyzing cyclic patterns using the cosine function often suffers from a multiple-solution problem. To address this, researchers have reformulated the cosine function as a combination of sine and cosine terms. Although this reformulation simplifies computation and resolves the multiple-solution issue, it complicates parameter interpretation and makes it difficult to assess how individual predictors influence features of the cyclic pattern. To bridge this gap, we propose a two-stage hybrid Bayesian approach that directly models cyclic pattern features while enabling evaluation of individual predictor effects. Through simulation studies, we demonstrate that the proposed method yields negligible bias and acceptable coverage rates. (PsycInfo Database Record (c) 2026 APA, all rights reserved).