Abstract:

“Trends” and “dynamics” represent two significant themes in longitudinal research. To address the challenges associated with trends and dynamics, researchers frequently utilize panel data or intensive longitudinal data to gather information, allowing for the development of various statistical models.

The trends study analyzes systematic changes and usually operates at the between-person level. It illustrates the general developmental trajectory while acknowledging individual differences. To effectively capture these general trends, researchers often use panel data, as it involves wide intervals and prolonged periods of data collection. A commonly employed model for this purpose is the latent growth model (LGM) combined with a multilevel model (MLM). In contrast, the dynamic study focuses on temporal changes within individuals, typically at the within-person level. It examines autoregressive and cross-lagged relationships from earlier time points to later ones. Both panel data and intensive longitudinal data could address dynamic issues because they allow for the measurement wave over short time intervals and necessitate a large number of measurements. Cross-lagged panel models (CLPM) are frequently used to analyze dynamics for panel data, while time series analysis and dynamic structural equation models (DSEM) are commonly applied to intensive longitudinal data.

As research questions become more intricate, we rely on models that integrate trends and dynamics, yielding numerous integrated models. For panel data, this includes the random intercept cross-lagged model (RI-CLPM), autoregressive latent trajectory model (ALT), and latent curve model with structural residuals (LCM-SR), among others, to provide a comprehensive approach to addressing the interplay of trends and dynamics. In the context of intensive longitudinal data, where stationary is a preassumption for time series modeling, models incorporating the detrending process have been developed, such as the dynamic structural equation model (DSEM) and residual dynamic equation model (RDSEM), etc.

We utilized empirical data from the 2013 Health and Retirement Study (HRS) to demonstrate the practical application of various longitudinal models. Our findings revealed that the integrated models, such as ALT and LCM-SR, exhibited superior model fit. This suggests that there are developmental trends that must be accounted for. The ALT model displayed significant autoregressive and cross-lagged relationships among the target variables, whereas the LCM-SR models did not.

In conclusion, we compared various longitudinal models and provided practical recommendations. First, researchers should determine the appropriate data collection paradigm to employ. When the number of measurement waves is ten or fewer and the time intervals are large, panel data is suitable; otherwise, an alternative approach should be considered. The long format is also suggested for intensive longitudinal data. Second, since the stationary is crucial in dynamic research, it is essential to assess trends. Panel data can be analyzed for trends using LGM or MLM with time covariates, while intensive longitudinal data (through time series analysis) should employ stationary tests. Descriptive statistics can also provide valuable insights. If trends are present, panel data should utilize an integrated model that encompasses both trends and dynamics, whereas intensive longitudinal data should adopt detrending models. In the absence of trends, direct dynamic modeling can be applied. Specifically, if the goal is to distinguish between trends and dynamics, researchers should consider residual models such as RI-CLPM, LCM-SR, and RDSEM. Conversely, for research emphasizing dynamics, cumulative models like ALT and DSEM should be applied.

Key words: longitudinal research, trends, dynamics, panel data, intensive longitudinal data, model selection