[R-sig-eco] Finding the largest kink

[Philip Dixon]

Matt,

When you ask "the question is how to pull out the number that is the 
(largest) kink.", are you trying to find the largest first derivative or 
the largest second derivative?

The x at which the first derivative is largest in magnitude will 
identify when the population changes most rapidly.
The x at which the first derivative is most negative will identify when 
the population drops the fastest.
The x at which to second derivative is the most negative will correspond 
to the biggest negative kink in the population trend, i.e. biggest 
change in trend.

The theory of penalized smoothing splines can be extended to predict 
derivatives.  The only thing to be careful about is to fit a high order 
smoothing spline to the data.  General recommendation is order = desired 
derivative + 1 or +2.  I usually use +2.   If you want to estimate 
second derivatives smoothly, that means fitting a quartic smoothing spline.

predict.smooth.Pspline() in the pspline package predicts derivatives 
from a smooth.Pspline object.

Best wishes,
Philip Dixon