MSc Statistics Defence: Regression Splines For Longitudinal Data

Denys Kelly, M.Sc. Project Presentation

Longitudinal studies are abundant in the world of research. These studies follow and take measurements from the same experimental unit over time and, therefore, observations within experimental units are correlated. Many of these studies result in data which are non-linear. Regression splines are a useful tool for modeling non-linear trends in data. This project compared three methods of applying regressions splines to longitudinal datasets. Firstly, a naive multivariate adaptive regression spline (MARS) approach was explored. This procedure is naive because it does not account for correlation within experimental units. Because of this, even though this method modelled data well, it is not recommended for longitudinal datasets. The multivariate adaptive splines for analysis of longitudinal data (MASAL) procedure was then explored. This method modifies the MARS procedure to account for correlated outcomes within experimental units. This method performed well. However, the function currently available for the MASAL procedure could use some modifications. Finally, regression spline mixed models were used with three different knot placements. This method consistently performed the best. However, for this procedure regression spline knots had to be selected in advance. Since the resulting models varied depending on knot selection, future work should look into creating an optimal knot placement strategy for this method.

A copy of the project is available (pdf format) from Susan McCormick for examination and comment.