Integrated Trend and Lagged Modeling of Multi-Subject, Multilevel, and Short Time Series

Trends represent systematic intra-individual variations that occur over slower time scales that, if unaccounted, are known to yield biases in estimation of momentary change patterns captured by time series models. The applicability of detrending methods has rarely been assessed in the context of multi-level longitudinal panel data, namely, nested data structures with relatively few measurements. This paper evaluated the efficacy of a series of two-stage detrending methods against a single-stage Bayesian approach in fitting multi-level nonlinear growth curve models with autoregressive residuals (ml-GAR) with random effects in both the growth and autoregressive processes. Monte Carlo simulation studies revealed that the single-stage Bayesian approach, in contrast to two-stage approaches, exhibited satisfactory properties with as few as five time points when the number of individuals was large (e.g., 500 individuals). It still outperformed alternative two-stage approaches when correlated random effects between the trend and autoregressive processes were misspecified as a diagonal random effect structure. Empirical results from the Early Childhood Longitudinal Study–Kindergarten Class (ECLS-K) data suggested substantial deviations in conclusions regarding children’s reading ability using two-stage in comparison to single-stage approaches, thus highlighting the importance of simultaneous modeling of trends and intraindividual variability whenever feasible.