# SiZer: Calculate SiZer Map In SiZer: Significant Zero Crossings

 SiZer R Documentation

## Calculate SiZer Map

### Description

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

### Usage

```SiZer(
x,
y,
h = NA,
x.grid = NA,
degree = NA,
derv = 1,
grid.length = 41,
quiet = TRUE
)
```

### 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 `degree` The degree of the local weighted polynomial used to smooth the data. This must be greater than or equal to `derv`. `derv` The order of derivative for which to make the SiZer map. `grid.length` The default length of the `h.grid` or `x.grid` if the length of either is not given. `quiet` Should diagnostic messages be suppressed? Defaults to TRUE.

### 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 list object of type SiZer 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.

`plot.SiZer`, `locally.weighted.polynomial`

### Examples

```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, grid.length=21)
plot(SiZer.1)
plot(SiZer.1, ggplot2=TRUE)

# Calculate the SiZer map for the second derivative
SiZer.2 <- SiZer(x, y, h=c(.5,10), degree=2, derv=2, grid.length=21);
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)

```

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