cpt.reg: Identifying Changes in Regression

In changepoint: Methods for Changepoint Detection

Identifying Changes in Regression

Description

Calculates the optimal position and (potentially) number of changepoints in regression structure for data using the user specified method.

Usage

  cpt.reg(data, penalty="MBIC", pen.value=0, method="PELT", test.stat="Normal",
    class=TRUE, param.estimates=TRUE, shape=0, minseglen=3, tol=1e-07)

Arguments

data	A matrix/array or ts object containing the data to fit the models to. Col1: the dependent variable, Col2+: regressors. A check is performed validate (or include if not) that an intercept regressor is included.
penalty	Choice of penalty, see penalty_decision.
pen.value	Additional values to be used in evaluating the penalty.
method	Choice changepoint algorithm. Either "AMOC" (at least one changepoint) or "PELT" (pruned exact linear time) method. Default is "PELT".
test.stat	Test statistic used for regression fit. Currently only "Normal" is supported which assumes a Normal distribution for the errors and fits using Residual Sum of Squares.
class	Logical. If TRUE then an oblect of class 'cpt.reg' is returned.
param.estimates	Logical. If TRUE and class=TRUE then parameter estimates are returned.
shape	Additional parameters used in the cost function. If dist="Normal", then shape is a single numeric variable that define the cost function to be: * shape < 0 : the residual sum of squares (i.e. quadratic cost). * shape = 0 : -2 * logLik (i.e. -2 * maximum likelihood value). Default. * shape > 0 : -2 * maximum likelihood value with variance=shape.
minseglen	Positive integer giving the minimum segment length (no. of observations between changes). Default is set at 3, however checks (and adjustements where applicable) are performed to ensure this is not smaller than the number of regressors.
tol	Tolerance for the 'qr' decomposition. Default is 1e-7. See lm.fit

Details

This function is used to find change in linear regression structure for data. The changes are found using the method supplied wihich can be single changepoint (AMOC) or multiple changepoints (PELT). A changepoint is denoted as the last observation of the segment / regime.

Value

If class=TRUE then an object of S4 class "cpt.reg" is returned. The slot cpts contains the changepoints that are returned. For class=FALSE the changepoint positions are returned, along with supplementary information about the fit detailed below. (This info is mainly used for bug fixing.)

If data is a matrix, then a vector/list/cpt.reg is returned depending on the of method. If data is a 3D array (multiple data sets, with total number of data sets = dim1 and each data set of the same size) then a list is returned where each element is either a vector/list/cpt.reg corresponding to the fit on each data set in the order they appear in the array.

If method="AMOC" & dist="Normal" then a list is returned with:

cpts: changepoint position.

pen.value: penalty value.

If method="PELT" & dist="Normal" then a list is returned with:

cpts: changepoint positions.

lastchangecpts: index of last changepoint according to optimal sequential fit.

lastchangelike: cost at last changepont according to optimal sequential fit.

ncpts: number of changepoints according to optimal squential fit.

Author(s)

Rebecca Killick, Simon Taylor

References

PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598

MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.

See Also

cpt.mean, penalty_decision, plot-methods, cpt, lm.fit

Examples

## Trend change
set.seed(1)
  x <- 1:200
  beta0 <- rep(c(0,100,50,0),each=50)
  beta1 <- rep(c(1,-1,0,0.25),each=50)
  y <- beta0 + beta1*x + rnorm(200)
  data <- cbind(y,1,x)

  out <- cpt.reg(data, method="PELT", minseglen=5, penalty="MBIC", test.stat="Normal")
  cpts(out)      ##changepoints
  param.est(out) ##parameter estimates (rows: beta estimates per segment)
  plot(out)      ##plot of fit



  ## Seasonal change, period 12
  n=100
indicator=rep(1,n)
trend=1:n
seasonal=cos(2*pi*(1:n -6)/12) # yearly, peak in summer
cpt.s = c(rep(0,floor(n/4)), rep(2, floor(n/4)), rep(1, floor(n/4)),rep(0,n-3*floor(n/4)))
##3 Alternating Cpts
y=0.1*cpt.s*1:n+cos(2*pi*(1:n -6)/12)+rnorm(n)
data=cbind(y,indicator,trend,seasonal)
out=cpt.reg(data, minseglen=12)
plot(out,cpt.width=3)
cpts(out)
param.est(out) ## column order of estimates matches the column order of inputs

changepoint documentation built on Nov. 4, 2024, 9:06 a.m.