changepoint (version 0.3)

single.reg.norm: Single Change in Regression - Normal Data

Description

Calculates the scaled log-likelihood (assuming the errors are zero-mean normally distributed) for all possible changepoint locations and returns the single most probable (max).

Usage

single.reg.norm(data, penalty="SIC",value=0,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

class

Logical. If TRUE then an object of class cpt is returned. If FALSE a vector 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.reg" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. 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 a number 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 a single change in regression for errors that are assumed to be normally distributed with zero mean. The value returned is the result of testing H0:no change in regression against H1: single change in regression using the log of the likelihood ratio statistic coupled with the penalty supplied.

References

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

See Also

cpt.reg,single.mean.norm,single.meanvar.norm,single.var.norm,cpt.reg

Examples

# Example of a change in regression at 100 in simulated normal data
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)
single.reg.norm(data,penalty="SIC",class=FALSE) # returns 100 to show that the null hypothesis was rejected and the change in regression is at 100
ans=single.reg.norm(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 a data matrix containing 2 rows, row 1 has a change in regression and row 2 had no change in regression
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)
data1=cbind(ynoise,1,x)
x=1:250
y=0.01*x+1
ynoise=y+rnorm(250,0,0.2)
data2=cbind(ynoise,1,x)

z=array(0,dim=c(2,250,3)) # note that the same model is fitted to all datasets
z[1,,]=data1
z[2,,]=data2
single.reg.norm(z,penalty="SIC",class=FALSE) # returns vector c(100,250) which shows that the first dataset has a change in regression at 100 and the second dataset rejected H1 and has no change in regression
ans=single.reg.norm(z,penalty="Manual",value="diffparam*log(n)") 
cpts(ans[[1]]) # test using a manual penalty which is the same as the SIC penalty for this example
cpts(ans[[2]]) # result is the same as above, c(100, 250) and 250.