changepoint (version 0.3)

binseg.reg.norm: Multiple Changes in Regression using Binary Segmentation method - Normal Errors

Description

Calculates the optimal positioning and number of changepoints for regression data with zero-mean Normal errors using Binary Segmentation method. Note that this is an approximate method.

Usage

binseg.reg.norm(data, Q=5, pen=0)

Arguments

data

A matrix or 3-d array containing the data within which you wish to find a changepoint. If data is a 3-d array, each first dimension is considered a separate dataset. Within each dataset the first column is considered the response and the further columns

Q

Numeric value of the maximum number of changepoints you wish to search for, default is 5.

pen

Numeric value of the linear penalty function. This value is used in the decision as to the optimal number of changepoints.

Value

• A list is returned containing the following items
• cps
  2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row.
• op.cpts
  The optimal changepoint locations for the penalty supplied.
• pen
  Penalty used to find the optimal number of changepoints.

Details

This function is used to find a multiple changes in regression for data that is assumed to have zero-mean normally distributed errors. The value returned is the result of finding the optimal location of up to Q changepoints using the log of the likelihood ratio statistic. Once all changepoint locations have been calculated, the optimal number of changepoints is decided using pen as the penalty function.

References

Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507--512

Change in regression: Chen, J. and Gupta, A. K. (2000) Parametric statistical change point analysis, Birkhauser

See Also

binseg.mean.norm,binseg.var.norm,binseg.meanvar.norm,cpt.reg,PELT.reg.norm,multiple.reg.norm,single.reg.norm,segneigh.reg.norm

Examples

# Example of multiple changes in regression at 100,250 in simulated data with zero-mean normal errors
set.seed(1)
x=1:400
y=c(0.01*x[1:100],3.5-0.02*x[101:250],-15+0.05*x[251:400])
ynoise=y+rnorm(400,0,0.2)
yx=cbind(ynoise,1,x)
binseg.reg.norm(yx,Q=5,pen=4*log(400)) # returns optimal number as 2 and the locations as c(100,250)
binseg.reg.norm(yx,Q=1,pen=4*log(400)) # returns optimal number as 1 as this is the maximum number of changepoints it can find.  If you get the maximum number, you need to increase Q until this is not the case.

# Example no change in regression
set.seed(10)
x=1:400
y=0.01*x
ynoise=y+rnorm(400,0,0.2)
yx=cbind(ynoise,1,x)
binseg.reg.norm(yx,Q=5,pen=4*log(400)) # returns optimal number as 0