hdMTD (version 0.1.1)

MTDest: EM estimation of MTD parameters

Description

Estimation of MTD parameters through the Expectation Maximization (EM) algorithm.

Usage

MTDest(
  X,
  S,
  M = 0.01,
  init,
  iter = FALSE,
  nIter = 100,
  A = NULL,
  oscillations = FALSE
)

Value

A list with the estimated parameters of the MTD model.

Arguments

X

A vector or single-column data frame containing an MTD chain sample (X[1] is the most recent).

S

A numeric vector of positive integers. Typically, S represents a set of relevant lags.

M

A stopping point for the EM algorithm. If M=NULL the algorithm will run for a total of nIter iteractions.

init

A list with initial parameters: p0 (optional), lambdas (required), pj (required). The entries in lambdas are weights for the distribution p0 and the distributions present in the list pj. Therefore, the order in which the elements appear in the vector lambdas is important for correct assignment. Please refer to the Details section for more information.

iter

Logical. If TRUE, returns the number of iterations of the algorithm, that is, the number of times the initial parameters were updated.

nIter

An integer positive number with the maximum number of iterations.

A

A vector with positive integers representing the state space. If not informed, this function will set A=unique(X).

oscillations

Logical. If TRUE, the function will return the estimated oscillations for the updated model along with the estimated parameters.

Details

Regarding the M parameter: it functions as a stopping criterion within the EM algorithm. When the difference between the log-likelihood computed with the newly estimated parameters and that computed with the previous parameters falls below M, the algorithm halts. Nevertheless, if the value of nIter (which represents the maximum number of iterations) is smaller than the number of iterations required to meet the M criterion, the algorithm will conclude its execution when nIter is reached. To ensure that the M criterion is effectively utilized, we recommend using a higher value for nIter, which is set to a default of 100.

Concerning the init parameter, it is expected to be a list comprising either 2 or 3 entries. These entries consist of: an optional vector named p0, representing an independent distribution (the probability in the first entry of p0 must be that of the smallest element in A and so on), a required list of matrices pj, containing a stochastic matrix for each element of S ( the first matrix must refer to the smallest element of S and so on), and a vector named lambdas representing the weights, the first entry must be the weight for p0, and then one entry for each element in pj list. If your MTD model does not have an independent distribution p0, set init$lambda[1]=0.

References

Lebre, Sophie and Bourguignon, Pierre-Yves. (2008). An EM algorithm for estimation in the Mixture Transition Distribution model. Journal of Statistical Computation and Simulation, 78(1), 1-15. tools:::Rd_expr_doi("10.1080/00949650701266666")

Examples

# Simulating data.
# Model:
MTD <- MTDmodel(Lambda=c(1,10),A=c(0,1),lam0=0.01)
# Sampling a chain:
X <- hdMTD::perfectSample(MTD,N=2000)

# Initial Parameters:
init <- list('p0'=c(0.4,0.6),'lambdas'=c(0.05,0.45,0.5),
  'pj'=list(matrix(c(0.2,0.8,0.45,0.55),byrow = TRUE,ncol=2),
   matrix(c(0.25,0.75,0.3,0.7),byrow = TRUE,ncol=2)))

# MTDest() ------------------------------------
MTDest(X,S=c(1,10),M=1,init)
MTDest(X,S=c(1,10),init=init,iter = TRUE)
MTDest(X,S=c(1,10),init=init,iter = TRUE,nIter=5)
MTDest(X,S=c(1,10),init=init,oscillations = TRUE)