R help - Aug 2015 - Piecewise (segmented) linear regression with center section slope constraint

Hi,

I'm working on a way to predict the electricity consumption of electrically
heated buildings as a function of outdoor air temperature. I've identified a
three-segment linear model as a candidate for a good fit, with the slope of
the center section constrained to zero. I'm working with the segmented
package. I've searched some of the other posts on this forum and they've
been very helpful, but they don't address my big sticking point: how do I
constrain the slope of the center section of the model to 0, rather than the
left or right section?

Below is a script with simulated data and my first attempt at fitting the
model. You should be able to copy, paste, and run it. Thanks in advance.
Drew

# three-piece segmented regression
# center section constrained to slope of 0.


# simulate and plot data
T<- 1:100
energy<- 100+75*pmax(55-T,0)+25*pmax(T-70,0)+150*rnorm(50)
plot(T, energy)

# create a linear model
model <- lm(energy~T)
#print(summary(model))

# start segmented regression
library(segmented)
seg_model <- segmented(model, seg.Z = ~ T, psi = list(T = c(52, 71)))
print(summary(seg_model))
print(seg_model$psi)
print(slope(seg_model))

# plot regression lines
fitted_energy <- fitted(seg_model)
regression_model <- data.frame(Temperature = T, kWh = fitted_energy)
lines(x = T, y = fitted_energy, col = 1)

# try constrained regression
TT<- -T   # change signs of independent variable
model <- lm(energy~1)  # constrain slope
seg_model <- segmented(model, seg.Z = ~ TT, psi = list(TT = c(-71, -52)))
print(summary(seg_model))
print(seg_model$psi)
print(slope(seg_model))

# plot constrained regression 
fitted_energy <- fitted(seg_model)
regression_model <- data.frame(Temperature = T, kWh = fitted_energy)
lines(x = T, y = fitted_energy, col = 2)



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This posting on StackOverflow might be useful to you.
http://stackoverflow.com/questions/13810607/in-r-package-segmented-how-could-i-set-the-slope-of-one-of-lines-in-the-model

Jean

On Thu, Aug 6, 2015 at 3:01 PM, Drew Morrison <dmorrison at
seventhwave.org>
wrote:
> Hi,
>
> I'm working on a way to predict the electricity consumption of
electrically
> heated buildings as a function of outdoor air temperature. I've
identified
> a
> three-segment linear model as a candidate for a good fit, with the slope of
> the center section constrained to zero. I'm working with the segmented
> package. I've searched some of the other posts on this forum and
they've
> been very helpful, but they don't address my big sticking point: how do
I
> constrain the slope of the center section of the model to 0, rather than
> the
> left or right section?
>
> Below is a script with simulated data and my first attempt at fitting the
> model. You should be able to copy, paste, and run it. Thanks in advance.
> Drew
>
> # three-piece segmented regression
> # center section constrained to slope of 0.
>
>
> # simulate and plot data
> T<- 1:100
> energy<- 100+75*pmax(55-T,0)+25*pmax(T-70,0)+150*rnorm(50)
> plot(T, energy)
>
> # create a linear model
> model <- lm(energy~T)
> #print(summary(model))
>
> # start segmented regression
> library(segmented)
> seg_model <- segmented(model, seg.Z = ~ T, psi = list(T = c(52, 71)))
> print(summary(seg_model))
> print(seg_model$psi)
> print(slope(seg_model))
>
> # plot regression lines
> fitted_energy <- fitted(seg_model)
> regression_model <- data.frame(Temperature = T, kWh = fitted_energy)
> lines(x = T, y = fitted_energy, col = 1)
>
> # try constrained regression
> TT<- -T   # change signs of independent variable
> model <- lm(energy~1)  # constrain slope
> seg_model <- segmented(model, seg.Z = ~ TT, psi = list(TT = c(-71,
-52)))
> print(summary(seg_model))
> print(seg_model$psi)
> print(slope(seg_model))
>
> # plot constrained regression
> fitted_energy <- fitted(seg_model)
> regression_model <- data.frame(Temperature = T, kWh = fitted_energy)
> lines(x = T, y = fitted_energy, col = 2)
>
>
>
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> View this message in context:
>
http://r.789695.n4.nabble.com/Piecewise-segmented-linear-regression-with-center-section-slope-constraint-tp4710839.html
> Sent from the R help mailing list archive at Nabble.com.
>
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Thanks, Jean. I've actually looked at that source before. The issue is that
I
can't constrain the slope of the /center/ section to be zero - in fact,
I've
applied similar code to a three-segment regression and I can get a zero
slope either of the two sides, but not in the middle.

Here's a list of the main resources I've consulted so far:

https://climateecology.wordpress.com/2012/08/19/r-for-ecologists-putting-together-a-piecewise-regression/

http://www.stackoverflow.dluat.com/questions/30060278/creating-piecewise-linear-regression-with-flat-slope-in-r

https://rpubs.com/MarkusLoew/12164



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