[R] Piecewise Regression with a known slope
Jarrett Byrnes
jebyrnes at ucdavis.edu
Sun Jul 29 23:22:05 CEST 2007
Hey, all. I'm working on a data set with a broken stick linear
regression where I know one of the two slopes. It is a negative
linear function until the line intersects with the x-axis, at which
point it becomes 0. It is not a nonlinear asymptotic function, and,
indeed, using negative exponential or logistic types of fits as an
approximation has tended to lead to an under or overestimation of
values. I am also very interested to know just what the breakpoint
in the data is.
Essentially
if x<psi y = a + bx + error, where b is negative
else y=0+error
and I want to know the value of psi, as well as a and b. The error
is also most likely gamma distributed, as values<0 are not possible
(nutrient concentrations).
I have attempted to use the segmented package, specifying something
close to the visually estimated breakpoint as the value of psi, but
it continues to return fits with a breakpoint that occurs somewhere
in the middle of the linear portion of the line, and the slope and
intercept of the second half of the regression is not 0.
Is there either a package that exists that will allow me to estimate
such a model, or a function that I can use for optim or nlm (I admit,
I am a rank novice at coding such functions).
Thanks so much!
-Jarrett
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