Higher order multivariate Markov chain class — hommc-class • markovchain

The S4 class of the higher order multivariate Markov chains of Ching, Ng and Fung (2008), fitted by fitHighOrderMultivarMC(): the distribution of the next state of each of \(s\) sequences is a weighted sum, over the sequences and the lags, of transition matrices applied to their past states.

Slots

order: The order of the chain (number of lags).
states: The states, common to all the sequences.
P: A three-dimensional array of \(s^2\) times order transition matrices, one for each pair of sequences and lag.
Lambda: The weights of the matrices in P, in the same order.
byrow: Logical: are the matrices stochastic by rows (TRUE) or by columns (FALSE, as returned by fitHighOrderMultivarMC())?
name: Optional name of the object.

References

Ching, W.-K., Ng, M. K. and Fung, E. S. (2008). Higher-order multivariate Markov chains and their applications. Linear Algebra and its Applications 428(2-3), 492-507. doi:10.1016/j.laa.2007.05.021

Author

Giorgio Spedicato, Deepak Yadav

Examples

statesName <- c("a", "b")

P <- array(0, dim = c(2, 2, 4), dimnames = list(statesName, statesName))
P[,,1] <- matrix(c(0, 1, 1/3, 2/3), byrow = FALSE, nrow = 2)
P[,,2] <- matrix(c(1/4, 3/4, 0, 1), byrow = FALSE, nrow = 2)
P[,,3] <- matrix(c(1, 0, 1/3, 2/3), byrow = FALSE, nrow = 2)
P[,,4] <- matrix(c(3/4, 1/4, 0, 1), byrow = FALSE, nrow = 2)

Lambda <- c(0.8, 0.2, 0.3, 0.7)

ob <- new("hommc", order = 1, states = statesName, P = P, 
          Lambda = Lambda, byrow = FALSE, name = "FOMMC")