Well, I knew that beta had to be negative, and that, based on the spline plots, the join point was around 15.  So I just used -1 for beta, and solved for gamma, given x0 was 15.  To get alpha, I picked something near the median value of all the points.  A little sensitivity analysis on alpha revealed that the final estimates were stable across all the values I tried.   I guess the key is using the plots to get an approximate value for x0, so that the ratio between beta and gamma was about twice that value.   SteveDenham ... View more