Simultaneous confidence intervals for transition probabilities

Simultaneous confidence intervals for the rows of an estimated transition matrix, each row being a multinomial proportion, by the method of Sison and Glaz (1995) in the implementation of May and Johnson (2000).

Usage

multinomialConfidenceIntervals(
  transitionMatrix,
  countsTransitionMatrix,
  confidencelevel = 0.95
)

Arguments

transitionMatrix

The estimated transition matrix.

countsTransitionMatrix

The matrix of transition counts from which transitionMatrix was estimated (see createSequenceMatrix()).

confidencelevel

Confidence level (default 0.95).

Value

A list with confidenceLevel, lowerEndpointMatrix and upperEndpointMatrix, the latter two with the dimnames of transitionMatrix.

References

Sison, C. P. and Glaz, J. (1995). Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association 90, 366-369.

May, W. L. and Johnson, W. D. (2000). Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells. Journal of Statistical Software 5(6).

See also

markovchainFit(), whose method = "mle" gives intervals for each probability separately rather than simultaneous ones for each row.

Examples

seq <- c("a", "b", "a", "a", "a", "a", "b", "a", "b", "a", "b", "a", "a",
         "b", "b", "b", "a")
mcfit <- markovchainFit(data = seq, byrow = TRUE)
seqmat <- createSequenceMatrix(seq)
multinomialConfidenceIntervals(mcfit$estimate@transitionMatrix, seqmat, 0.95)
#> $confidenceLevel
#> [1] 0.95
#> 
#> $lowerEndpointMatrix
#>           a         b
#> a 0.2222222 0.3333333
#> b 0.5714286 0.1428571
#> 
#> $upperEndpointMatrix
#>           a         b
#> a 0.8111456 0.9222567
#> b 1.0000000 0.6839473
#>