Technical note: Estimating parameters of nonlinear segmented models.

The objective of this technical note is to develop an applied technique to estimate parameters using the Statistical Analysis System's nonlinear procedure (SAS PROC NLIN) for segmented models that have a change point or lag as one of the parameters. The goal is to select good starting values for the parameters near the global minimum or at least near a lower local minimum compared with what might be achieved using traditional starting values. The model used was f1 (t) = B1 + B4 if t < or = B3 and f2(t) = B1*exp[-B2*(t - B3)] + B4 if t > B3, where B1, B2, B3, and B4 are the parameters that require estimates, B3 is the change point or lag, and t = time. This technical note illustrates the solution when a traditional grid search for starting values is used and demonstrates a modified technique where starting values are systemically determined by fixing B3 over a range of reasonable values and then using the parameters from the solution with the lowest residual sums of squares as the starting values for the final solution. The modified method resulted in a lower square root of mean square error compared with the traditional method. The estimates for B3 (lag) were 3.5 for the modified method compared with 4.5 for the traditional method. This technique works well when using the SAS PROC NLIN procedure but can be modified to work with other statistical packages.