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Last data update: 2014.03.03

R: Fits a bent-cable model to the given data

bent.cable

R Documentation

Fits a bent-cable model to the given data

Description

Fits a bent-cable model to the given data by exhaustively searching the 2-dimensional parameter space to find the maximum likelihood estimators for α and γ.

Usage

bent.cable(x, y, grid.size=100)

Arguments

`x`	The independent variable
`y`	The dependent variable
`grid.size`	How many α and gamma values to examine. The total number of parameter combinations examined is `grid.size` squared.

Details

Fit the model which is essentially a piecewise linear model with a quadratic curve of length 2γ connecting the two linear pieces.

The reason for searching the space exhaustively is because the bent-cable model often has a likelihood surface with a very flat ridge instead of definite peak. While the exhaustive search is slow, at least it is possible to examine the contour plot of the likelihood surface.

Value

A list of 7 elements:

`log.likelihood`	A matrix of log-likelihood values.
`SSE`	A matrix of sum-of-square-error values.
`alphas`	A vector of alpha values examined.
`gammas`	A vector of gamma values examined.
`alpha`	The MLE estimate of alpha.
`gamma`	The MLE estimate of gamma.
`model`	The `lm` fit after alpha and gamma are known.

Author(s)

Derek Sonderegger

References

Chiu, G. S., R. Lockhart, and R. Routledge. 2006. Bent-cable regression theory and applications. Journal of the American Statistical Association 101:542-553.

Toms, J. D., and M. L. Lesperance. 2003. Piecewise regression: a tool for identifying ecological thresholds. Ecology 84:2034-2041.

Examples

data(Arkansas)
x <- Arkansas$year
y <- Arkansas$sqrt.mayflies

# For a more accurate estimate, increase grid.size
model <- bent.cable(x,y, grid.size=20)
plot(x,y)
x.grid <- seq(min(x), max(x), length=200)
lines(x.grid, predict(model, x.grid), col='red')

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(SiZer)
Loading required package: splines
Loading required package: boot
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SiZer/bent.cable.Rd_%03d_medium.png", width=480, height=480)
> ### Name: bent.cable
> ### Title: Fits a bent-cable model to the given data
> ### Aliases: bent.cable logLik.bent_cable predict.bent_cable
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(Arkansas)
> x <- Arkansas$year
> y <- Arkansas$sqrt.mayflies
> 
> # For a more accurate estimate, increase grid.size
> model <- bent.cable(x,y, grid.size=20)
> plot(x,y)
> x.grid <- seq(min(x), max(x), length=200)
> lines(x.grid, predict(model, x.grid), col='red')
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>