R: Various functions to perform statistical inference of DTMC

verifyMarkovProperty {markovchain} | R Documentation

## Various functions to perform statistical inference of DTMC

### Description

These functions verify the Markov property, assess the order and stationarity of the Markov chain.

This function tests whether an empirical transition matrix is statistically compatible with a theoretical one. It is a chi-square based test. In case a cell in the empirical transition matrix is >0 that is 0 in the theoretical transition matrix the null hypothesis is rejected.

Verifies that the s elements in the input list belongs to the same DTMC

### Usage

    verifyMarkovProperty(sequence, verbose = TRUE)

    assessOrder(sequence, verbose = TRUE)

    assessStationarity(sequence, nblocks, verbose = TRUE)

    verifyEmpiricalToTheoretical(data, object, verbose = TRUE)

    verifyHomogeneity(inputList, verbose = TRUE)

### Arguments

`sequence` | An empirical sequence.
`verbose` | Should test results be printed out?
`nblocks` | Number of blocks.
`data` | matrix, character or list to be converted in a raw transition matrix
`object` | a markovchain object
`inputList` | A list of items that can coerced to transition matrices

### Value

Verification result

a list with following slots: statistic (the chi - square statistic), dof (degrees of freedom), and corresponding p-value. In case a cell in the empirical transition matrix is >0 that is 0 in the theoretical transition matrix the null hypothesis is rejected. In that case a p-value of 0 and statistic and dof of NA are returned.

a list of transition matrices?

### Author(s)

Tae Seung Kang, Giorgio Alfredo Spedicato

### References

Anderson and Goodman.

### See Also

`markovchain`

### Examples

    sequence <- c("a", "b", "a", "a", "a", "a", "b", "a", "b",
                  "a", "b", "a", "a", "b", "b", "b", "a")
    mcFit <- markovchainFit(data = sequence, byrow = FALSE)
    verifyMarkovProperty(sequence)
    assessOrder(sequence)
    assessStationarity(sequence, 1)

    #Example taken from Kullback Kupperman Tests for Contingency Tables and Markov Chains

    sequence<-c(0,1,2,2,1,0,0,0,0,0,0,1,2,2,2,1,0,0,1,0,0,0,0,0,0,1,1,
    2,0,0,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,2,1,0,
    0,2,1,0,0,0,0,0,0,1,1,1,2,2,0,0,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,0,2,
    0,1,1,0,0,0,1,2,2,0,0,0,0,0,0,2,2,2,1,1,1,1,0,1,1,1,1,0,0,2,1,1,
    0,0,0,0,0,2,2,1,1,1,1,1,2,1,2,0,0,0,1,2,2,2,0,0,0,1,1)

    mc=matrix(c(5/8,1/4,1/8,1/4,1/2,1/4,1/4,3/8,3/8),byrow=TRUE, nrow=3)
    rownames(mc)<-colnames(mc)<-0:2; theoreticalMc<-as(mc, "markovchain")

    verifyEmpiricalToTheoretical(data=sequence,object=theoreticalMc)

    data(kullback)
    verifyHomogeneity(inputList=kullback,verbose=TRUE)

[Package markovchain version 0.8.6 Index]