When the Wrong Model Fits Better: Effect of Temporal Design On Trajectory Selection in Latent Growth Curve Models

Prevention researchers often collect longitudinal data in order to better understand how behaviors change across time and to determine if effects from intervention programs are maintained or decay once the program is over. Temporal design refers to the number of times the variables in a longitudinal study are measured as well as the spacing of these measurements. Selecting a good temporal design depends on knowing how and when the variables of interest change in order to ensure the variables are measured frequently enough and at the right times to capture effects. While most researchers give careful thought in planning their studies, an optimal temporal design may be impossible to achieve due to practical constraints (e.g., lack of funding, lack of staff, etc.) or because the characteristics of the variables of interest are not well known enough to determine what is an optimal temporal design. The current study examines the impact of temporal designs on trajectory selection in latent growth curve models. First, longitudinal data were simulated in SAS using different known functions including linear, quadratic, exponential decay, and logistic functions. Then samples were selected from the simulated data using different, common temporal designs that varied the number of measurements as well as the spacing of the measurements. For example, five equally spaced measurements across the length of the study versus seven measurements where six were taken in rapid succession at the beginning of the study and the seventh was taken at the end. Next, latent growth curve models based on the different functions were fit to the samples using Mplus and fit statistics such as the RMSEA, CFI, Akaike Information Criterion, and Bayesian Information Criterion were examined to determine model fit. Initial results show that temporal design has a large impact on model fit and can cause an incorrect model (i.e., a model with a trajectory that is not the same as the one the data were created from) to fit the data better than the correct latent growth curve model based on common fit indices. For example, for one temporal design a quadratic growth model fit data created from an exponential decay function better than an exponential decay growth model. These results have important implications for prevention researchers as they show the danger of selecting temporal design based on convenience rather than variable and participant characteristics. Other implications and limitations of the study are presented as well.