Deborah Hurley, MSPH, James R Hussey, PhD, Robert McKeown, PhD, and Cheryl Addy, PhD. Department of Epidemiology and Biostatistics, University of South Carolina, Norman J. Arnold School of Public Health, 800 Sumter Street, Columbia, SC 29208, 803-777-5331, hurleyd@gwm.sc.edu

Spline modeling may provide a better fit to data than polynomial or categorical models. There is no one best approach, however, as some methods may produce better results for predicted values (e.g., smaller confidence intervals) than others, depending on the data. To address this, a simulation study was undertaken. Data were simulated to create 30 scenarios (5 data structures, 3 sample sizes, 2 standard deviations). Six regression models were evaluated for each of the 30 scenarios: simple linear regression (SLR), polynomial regression (quadratic and cubic), and spline regression (linear, quadratic and cubic). Various criteria were compared for each scenario to assess model “fit” verses model simplicity: confidence interval coverage on the predicted values, confidence interval widths, mean squared error (MSE), and the PRESS and R2 statistics. Results indicated that the best choice of a modeling method should take into account preliminary plots and the estimated standard deviation. Splines are most appropriate when the plots of the data clearly indicate that they are needed (i.e., when the standard deviation is small and we can detect knots and changes in structure. When the plots do not show much detail (i.e., when the standard deviation is large), it is generally better to use a simpler model (e.g., polynomial). Results also reinforce the need to look at a plot of the predicted values for your model, as some of the usual selection criteria (MSE, PRESS, R2) can give similar results for various models, but the coverage for these models may be diverse.

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