changepoint (version 0.3)

cpt.reg: Identifying Changes in Regression

Description

Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.

Usage

cpt.reg(data,penalty="SIC",value=0,method="AMOC",Q=5,dist="Normal",class=TRUE,param.estimates=TRUE)

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

penalty

Choice of "None", "SIC", "BIC", "AIC", "Hannan-Quinn", "Asymptotic" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the value parameter. If Asymptotic is specified, the theoretical type I error is contained in the value

value

The theoretical type I error e.g.0.05 when using the Asymptotic penalty. The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, n

method

Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg".

Q

The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method.

dist

The assumed distribution of the data. Currently only "Normal" is supported.

class

Logical. If TRUE then an object of class cpt is returned.

param.estimates

Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.

Value

• If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. The structure of cpts is as follows.

  If data is an nxp matrix (single dataset) then a single value is returned:

• cpt
  The most probable location of a changepoint if H0 was rejected or n if H1 was rejected.
• If data is an mxnxp matrix (multiple datasets) then a vector is returned:
• cpt
  Vector of length m containing where each element is the result of the test for data[m,,]. If cpt[m] is less than n then it is the most probable location of a changepoint under H1. Otherwise cpt[m] has the value n and indicates that H1 was rejected.

Details

This function is used to find changes in regression for data that is assumed to be distributed as the dist parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods.

References

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

See Also

cpt.var,cpt.meanvar,cpt.mean,cpt.reg

Examples

# Example of a change in regression at 100 in simulated data with zero-mean normal errors
set.seed(1)
x=1:250
y=c(0.01*x[1:100],1.5-0.02*(x[101:250]-101))
ynoise=y+rnorm(250,0,0.2)
data=cbind(ynoise,1,x)
cpt.reg(data,penalty="SIC",class=FALSE) # returns 100 to show that the null hypothesis was rejected and the change in regression is at 100
ans=cpt.reg(data,penalty="Asymptotic",value=0.01) 
cpts(ans) # returns 100 to show that the null hypothesis was rejected, the change in regression is at 100 and we are 99% confident of this result

# 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)
cpt.reg(yx,method="BinSeg",penalty="Manual",value="4*log(n)",Q=5,class=FALSE) # returns optimal number of changepoints is 2, locations are 100,250.

# Example multiple datasets where the first has multiple changes in regression and the second has no change in regression
set.seed(1)
x1=1:400
y1=c(0.01*x1[1:100],3.5-0.02*x1[101:250],-15+0.05*x1[251:400])
ynoise1=y1+rnorm(400,0,0.2)
yx1=cbind(ynoise1,1,x1)

x2=1:400
y2=0.01*x2
ynoise2=y2+rnorm(400,0,0.2)
yx2=cbind(ynoise2,1,x2)

data=array(0,dim=c(2,400,3))
data[1,,]=yx1; data[2,,]=yx2

cpt.reg(data,method="SegNeigh",penalty="Asymptotic",value=0.01,Q=5,class=FALSE) # returns list that has two elements, the first has 2 changes in regression at 100,250 and the second has no changes in regression
ans=cpt.reg(data,method="PELT",penalty="Asymptotic",value=0.01) 
cpts(ans[[1]]) # same results as for the SegNeigh method.
cpts(ans[[2]]) # same results as for the SegNeigh method.