# Calculate SiZer Map

### Description

Calculates the SiZer map from a given set of X and Y variables.

### Usage

1 |

### Arguments

`x` |
data vector for the independent axis |

`y` |
data vector for the dependent axis |

`h` |
An integer representing how many bandwidths should be considered, or vector of length 2 representing the upper and lower limits h should take, or a vector of length greater than two indicating which bandwidths to examine. |

`x.grid` |
An integer representing how many bins to use along the x-axis, or a vector of length 2 representing the upper and lower limits the x-axis should take, or a vector of length greater than two indicating which x-values the derivative should be evaluated at. |

`grid.length` |
The default length of the |

`derv` |
The order of derivative for which to make the SiZer map. |

`degree` |
The degree of the local weighted polynomial used to smooth the data.
This must be greater than or equal to |

### Details

SiZer stands for the Significant Zero crossings of the derivative. There are two dominate approaches in smoothing bivariate data: locally weighted regression or penalized splines. Both approaches require the use of a 'bandwidth' parameter that controls how much smoothing should be done. Unfortunately there is no uniformly best bandwidth selection procedure. SiZer (Chaudhuri and Marron, 1999) is a procedure that looks across a range of bandwidths and classifies the p-th derivative of the smoother into one of three states: significantly increasing (blue), possibly zero (purple), or significantly negative (red).

### Value

Returns an SiZer object which has the following components:

`x.grid` |
Vector of x-values at which the derivative was evaluated. |

`h.grid` |
Vector of bandwidth values for which a smoothing function was calculated. |

`slopes` |
Matrix of what category a particular x-value and bandwidth falls into (Increasing=1, Possibly Zero=0, Decreasing=-1, Not Enough Data=2). |

### Author(s)

Derek Sonderegger

### References

Chaudhuri, P., and J. S. Marron. 1999. SiZer for exploration of structures in curves. Journal of the American Statistical Association 94:807-823.

Hannig, J., and J. S. Marron. 2006. Advanced distribution theory for SiZer. Journal of the American Statistical Association 101:484-499.

Sonderegger, D.L., Wang, H., Clements, W.H., and Noon, B.R. 2009. Using SiZer to detect thresholds in ecological data. Frontiers in Ecology and the Environment 7:190-195.

### See Also

`plot.SiZer`

, `locally.weighted.polynomial`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
data('Arkansas')
x <- Arkansas$year
y <- Arkansas$sqrt.mayflies
plot(x,y)
# Calculate the SiZer map for the first derivative
SiZer.1 <- SiZer(x, y, h=c(.5,10), degree=1, derv=1)
plot(SiZer.1)
# Calculate the SiZer map for the second derivative
SiZer.2 <- SiZer(x, y, h=c(.5,10), degree=2, derv=2);
plot(SiZer.2)
# By setting the grid.length larger, we get a more detailed SiZer
# map but it takes longer to compute.
#
# SiZer.3 <- SiZer(x, y, h=c(.5,10), grid.length=100, degree=1, derv=1)
# plot(SiZer.3)
``` |