OpenMx (version 2.7.9)

mxExpectationHiddenMarkov: Hidden Markov expectation

Description

Used in conjuction with mxFitFunctionML, this expectation can express a mixture model (with the transition matrix omitted) or a Hidden Markov model.

Usage

mxExpectationHiddenMarkov(components, initial="initial", transition=NULL,
		      ..., verbose=0L, scale=c('softmax','sum'))

Arguments

components

A character vector of model names.

initial

The name of the matrix or algebra column that specifies the initial probabilities.

transition

The name of the matrix or algebra that specifies the left stochastic transition probabilities.

...

Not used. Forces remaining arguments to be specified by name.

verbose

the level of runtime diagnostics

scale

How the probabilities are rescaled. For 'softmax', the coefficient-wise exponential is taken and then each column is divided by its column sum. For 'sum', each column is divided by its column sum.

Details

Parameters are estimated in the given scale. To obtain the initial column vector and left stochastic transition matrix in probability units then examine the expectation's output slot. mxGenerateData is not implemented for this type of expectation.

Examples

library(OpenMx)

start_prob <- c(.2,.4,.4)
transition_prob <- matrix(c(.8, .1, .1,
			.3, .6, .1,
			.1, .3, .6), 3, 3)
noise <- .5

  # simulate a trajectory
  state <- sample.int(3, 1, prob=transition_prob %*% start_prob)
  trail <- c(state)

  for (rep in 1:500) {
    state <- sample.int(3, 1, prob=transition_prob[,state])
    trail <- c(trail, state)
  }
  
  # add noise
  trailN <- sapply(trail, function(v) rnorm(1, mean=v, sd=sqrt(noise)))

  classes <- list()
  
  for (cl in 1:3) {
    classes[[cl]] <- mxModel(paste0("cl", cl), type="RAM",
                             manifestVars=c("ob"),
                             mxPath("one", "ob", value=cl, free=FALSE),
                             mxPath("ob", arrows=2, value=noise, free=FALSE),
                             mxFitFunctionML(vector=TRUE))
  }

  m1 <-  
    mxModel("hmm", classes,
            mxData(data.frame(ob=trailN), "raw"),
            mxMatrix(nrow=3, ncol=1,
                     labels=paste0('i',1:3), name="initial"),
            mxMatrix(nrow=length(classes), ncol=length(classes),
                     labels=paste0('t', 1:(length(classes) * length(classes))),
                     name="transition"),
            mxExpectationHiddenMarkov(
              components=sapply(classes, function(m) m$name),
              initial="initial",
              transition="transition", scale="softmax"),
            mxFitFunctionML())

  m1$transition$free[1:(length(classes)-1), 1:length(classes)] <- TRUE

m1 <- mxRun(m1)

summary(m1)

print(m1$expectation$output)