Flexible Treatment of Time-Varying Covariates with Time Unstructured Data

Time-varying covariates (TVCs) are a common component of growth models. Though mixed effect models (MEMs) and latent curve models (LCMs) are often seen as interchangeable, LCMs are generally more flexible for accommodating TVCs. Specifically, the standard MEM constrains the effect of TVCs across time-points whereas the typical LCM specification can estimate time-specific TVC effects, can include lagged TVC effects, or constrain some TVC effects based on theoretically appropriate phases. However, when data are time-unstructured, LCMs can have difficulty providing TVC effects whose interpretation aligns with typical research questions. This paper shows how MEMs can be adapted to yield TVC effects that mirror the flexibility of LCMs such that the model likelihoods are identical in ideal circumstances. We then extend this adaptation to the context of time-unstructured data where MEMs tend to be more flexible than LCMs. Examples and software code are provided to facilitate implementation of these methods.