Splines

Editor-In-Chief: Jacki Buros [mailto:jburos@perfuse.org]

= References =
 * Splines with parameters that can be explained to non-mathematicians Good overview by Roger Newson (King’s College, London, UK). Uses Stata syntax.

"Data were simulated for five different structures (patterns), using one dependent variable and one independent variable. Each of these five structures was generated with three different sample sizes (n), and two different standard deviations, for a total of 6 scenarios for each structure. For each scenario, 2000 simulated data sets were generated. Six different regression models were evaluated for each of the 30 scenarios. These models were simple linear regression (SLR), polynomial regression (quadratic and cubic), and spline regression (linear, quadratic and cubic)."
 * An Evaluation of Splines in Linear Regression by a group from University of SC led by Deborah Hurley, MSPH. Analysis in SAS. Group evaluates performance of spline regression on 5 sets of simulated datasets, each with a different underlying data structure. Goal is to see how well regression analysis with splines performs relative to linear and polynomial regression modeling techniques. An excerpt from the Methods section:
 * Concludes that, in general, model parameters (MSE, press statistic, and R2 statistic) choose the correct model irrespective of sample size. However, that more complex spline techniques result in a loss of precision. Splines may therefore be best suited for situations where the description of the shape of the distribution is of primary interest (ie, to adjust for a covariate or to test for theoretically-meaningful nonlinearities).


 * Regression Splines with Longitudinal Data by a group from University of Arkansas Medical Sciences led by Chan Hee Jo. Analysis in SAS.


 * Regression Splines: a Review by David Ruppert at Cornell University. Good set of lecture overheads with examples of various scenarios in which spline analysis is useful. Starts with the notion that splines are linear regression models that allow one to fit model parameters to nonparametric data structures. Examples include a linear spline, a polynomial spline, two additive spline models -- one with and one without interaction, and a measurement error model. Discusses techniques to determine the ideal number and placement of knots (least squares and penalized least squares goodness-of-fit statistics, cross-validation and generalized cross-validation), the estimation of derivatives, and interactions. Includes a slide on Bayesian interpretation.