The analysis of longitudinal data using mixed model L-splines
L-splines are a large family of smoothing splines defined in terms of a linear differential operator. This article develops L-splines within the context of linear mixed models and uses the resulting mixed model L-spline to analyze longitudinal data from a grassland experiment. In the spirit of time-series analysis, a periodic mixed model L-spline is developed, which partitions data into a smooth periodic component plus smooth long-term trend.
Welham, S. J.., Cullis, B. R., Kenward, M. J.. & Thompson, R. (2006). The analysis of longitudinal data using mixed model L-splines. Biometrics, 62 (2), 392-401.