# piecewise.linear: Creates a piecewise linear model In SiZer: Significant Zero Crossings

 piecewise.linear R Documentation

## 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
)
```

### 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.

### Value

A list of 5 elements is returned:

change.point

The estimate of α.

model

The resulting `lm` object once α 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.

### 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.

### See Also

The package `segmented` has a much more general implementation of this analysis and users should preferentially use that package.

### Examples

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

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

SiZer documentation built on July 10, 2022, 1:05 a.m.