Dear Jarrett,
If I understand correctly your post, your constraints may be achieved
straightforwardly in segmented. See the code below.
The error is also most likely gamma distributed..[SNIP]
The 'error' component can be specified in the 'initial' model by means of
the family argument in the glm() function
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, ..[SNIP]
Mhmm..you can specify different starting values and to assess the
differences in the 'final' estimates. However if you says ..it continues
to return fits with a breakpoint that occurs somewhere in the middle..
probably the ML estimate of the breakpoint is really in the middle.
Hope this helps you,
best,
vito
simulate data
n-50
x-1:n/n
y- 0-pmin(x-.5,0)+rnorm(50)*.03
plot(x,y) #This should be your scatterplot..
abline(0,0,lty=2)
o-lm(y~x) #or glm(y~x,family=..)
o1-segmented(o,seg.Z=~x,psi=list(x=.3))
slope(o1) #get the slope
points(x,fitted(o1),col=2)
#a parsimonious modelling: constrain right slope=0
o-lm(y~1)
xx- -x
o2-segmented(o,seg.Z=~xx,psi=list(xx=-.3))
slope(o2)
points(x,fitted(o2),col=2)
#now constrain \hat{\mu}(x)=0 for xpsi
o-lm(y~0)
o3-segmented(o,seg.Z=~xx,psi=list(xx=-.3))
slope(o3)
points(x,fitted(o3),col=3)
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 xpsi 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 values0 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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and provide commented, minimal, self-contained, reproducible code.
