Calculate SiZer Map

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.

See Also

plot.SiZer, locally.weighted.polynomial

Examples

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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)