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

## Description

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

## Usage

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

## 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 `h.grid` or `x.grid` if the length of either is not given. `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 `derv`.

## 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.

`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) ```

### Example output

```Loading required package: splines
[1] 0.5
[1] 0.5388846
[1] 0.5807932
[1] 0.625961
[1] 0.6746414
[1] 0.7271077
[1] 0.7836543
[1] 0.8445984
[1] 0.9102821
[1] 0.981074
[1] 1.057371
[1] 1.139602
[1] 1.228228
[1] 1.323746
[1] 1.426693
[1] 1.537646
[1] 1.657227
[1] 1.786108
[1] 1.925012
[1] 2.074719
[1] 2.236068
[1] 2.409965
[1] 2.597386
[1] 2.799383
[1] 3.017088
[1] 3.251725
[1] 3.504608
[1] 3.777159
[1] 4.070905
[1] 4.387496
[1] 4.728708
[1] 5.096456
[1] 5.492803
[1] 5.919973
[1] 6.380365
[1] 6.87656
[1] 7.411344
[1] 7.987718
[1] 8.608917
[1] 9.278425
[1] 10
[1] 0.5
[1] 0.5388846
[1] 0.5807932
[1] 0.625961
[1] 0.6746414
[1] 0.7271077
[1] 0.7836543
[1] 0.8445984
[1] 0.9102821
[1] 0.981074
[1] 1.057371
[1] 1.139602
[1] 1.228228
[1] 1.323746
[1] 1.426693
[1] 1.537646
[1] 1.657227
[1] 1.786108
[1] 1.925012
[1] 2.074719
[1] 2.236068
[1] 2.409965
[1] 2.597386
[1] 2.799383
[1] 3.017088
[1] 3.251725
[1] 3.504608
[1] 3.777159
[1] 4.070905
[1] 4.387496
[1] 4.728708
[1] 5.096456
[1] 5.492803
[1] 5.919973
[1] 6.380365
[1] 6.87656
[1] 7.411344
[1] 7.987718
[1] 8.608917
[1] 9.278425
[1] 10
```

SiZer documentation built on May 29, 2017, 12:57 p.m.