Symposia
Research Methods and Statistics
Steven M. Brunwasser, Ph.D.
Rowan University
Glassboro, New Jersey
Social scientists often use suboptimal strategies to model effects of continuous predictors. It is common, for example, to make rigid – and often unrealistic – linearity assumptions or to transform the continuous predictor into a less informative categorical variable. The purpose of this presentation is to demonstrate how restricted cubic splines (RCSs) allow one to model effects of continuous predictors flexibly while utilizing all information the variable provides. In the RCS approach, the modeler positions knots (or junctions) at specific values of the continuous predictor and captures change between the knots (k) using cubic functions, while the tails of the effect are constrained to be linear. This allows the estimated relation between the continuous predictor and outcome to take a highly flexible form with k-1 degrees of freedom. Despite desirable properties, the RCS approach is rarely utilized in structural equation modeling applications. This presentation will focus on two specific SEM-based applications of RCS modeling. First, I will demonstrate how the RCS approach can be used in latent growth curve (LGC) models to capture nonlinear time trends. LGC users often model nonlinear outcome trajectories using smooth polynomial functions (e.g., quadratic or cubic) or piecewise linear models. I will present the RCS model as an alternative approach that can better accommodate sharp changes in the rate of growth over time. Second, I will demonstrate the utility of the RCS approach when modeling effects of observed continuous predictors in LGC models when the appropriate function (e.g., linear, quadratic, etc.) is not known. I will show how the RCS approach could help limit residual confounding by more accurately estimating covariate effects. Finally, I will discuss strategies for selecting the number and placement of knots, and the importance of avoiding pitfalls (e.g., overfitting through data-driven determination of knot spacing). The presentation will include demonstrations using R software with both simulated and real data sets, including a randomized controlled trial (N=697; 8 time points) and a prospective cohort study (N=1913; 14 time points).