mixtools (version 0.3.0)

regmixEM.chgpt: EM Algorithm for Mixtures of Regressions with a Changepoint

Description

Returns EM algorithm output for a mixture of a regression with a changepoint and a simple linear regression.

Usage

regmixEM.chgpt(y, x, lambda = NULL, gamma = NULL, beta = NULL,
               sigma = NULL, k = 2, T = 3, t = NULL, 
               epsilon = 1e-08, maxit = 10000, verb = FALSE)

Arguments

y

An n-vector of response values.

x

An n-vector of predictor values. A column of ones is automatically appended to x.

lambda

Initial value of mixing proportions. Entries should sum to 1. If NULL, then lambda is random from uniform Dirichlet.

gamma

Initial value of gamma parameters for the changepoint component. Should be a 3-dimenstional vector. If NULL, then gamma has standard normal entries according to a binning method done on the data.

beta

Initial value of beta parameters for the simple linear regression component. Should be a 2-dimenstional vector. If NULL, then beta has standard normal entries according to a binning method done on the data.

sigma

A vector of standard deviations. If NULL, then 1/sigma$^2$ has random standard exponential entries according to a binning method done on the data.

k

Number of components. Currently, this value must be set equal to 2.

T

The number of values to leave off for the range of all possible changepoints to be tested.

t

Initial value of the changepoint to consider.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

• regmixEM.chgpt returns a list of class mixEM with items:
• lambda
  The final mixing proportions.
• gamma
  The final regression coefficients for the changepoint component.
• beta
  The final regression coefficients for the simple linear regression component.
• sigma
  The final standard deviations.
• cutpoint
  The estimated value for the changepoint in the changepoint component.
• loglik
  The final log-likelihood.
• posterior
  A nx2 matrix of posterior probabilities for observations.
• all.loglik
  A vector of each iteration's log-likelihood.
• restarts
  The number of times the algorithm restarted due to unacceptable choice of initial values.
• ft
  A character vector giving the name of the function.

See Also

regmixEM

Examples

## EM output for simulated data.
 
w<-rbinom(100, 1, .5)
cpt<-50
x<-sort(runif(100, 0, 10))
x1<-cbind(1, x)
xt<-cbind(x1, (x-x[cpt])*(x>x[cpt]))
beta<-c(5, -1)
gamma<-c(15, -1, 2)
y<-w*rnorm(100, mean = xt%*%gamma, sd = .1) + 
   (1-w)*rnorm(100, mean = x1%*%beta, sd = .1)
out<-regmixEM.chgpt(y = y, x = x, t = cpt, beta = beta, 
                    gamma = gamma, verb = TRUE, epsilon = 1e-03)
out