piecewise.linear: Creates a piecewise linear model

Description

Fit a degree 1 spline with 1 knot point where the location of the knot point is unknown.

Usage

piecewise.linear(
  x,
  y,
  middle = 1,
  CI = FALSE,
  bootstrap.samples = 1000,
  sig.level = 0.05
)

Value

A list of 5 elements is returned:

change.point: The estimate of \(\alpha\).
model: The resulting lm object once \(\alpha\) is known.
x: The x-values used.
y: The y-values used.
CI: Whether or not the confidence interval was calculated.
intervals: If the CIs where calculated, this is a matrix of the upper and lower intervals.

Arguments

x: Vector of data for the x-axis.
y: Vector of data for the y-axis
middle: A scalar in \([0,1]\). This represents the range that the change-point can occur in. \(0\) means the change-point must occur at the middle of the range of x-values. \(1\) means that the change-point can occur anywhere along the range of the x-values.
CI: Whether or not a bootstrap confidence interval should be calculated. Defaults to FALSE because the interval takes a non-trivial amount of time to calculate
bootstrap.samples: The number of bootstrap samples to take when calculating the CI.
sig.level: What significance level to use for the confidence intervals.

Details

The bootstrap samples are taken by resampling the raw data points. Sometimes a more appropriate bootstrap sample would be to calculate the residuals and then add a randomly selected residual to each y-value.

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

Run this code

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

model <- piecewise.linear(x,y, CI=FALSE)
plot(model)
print(model)
predict(model, 2001)

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