Estimates a non-homogeneous discrete time Markov chain, with one transition matrix for each pair of consecutive times, from a panel of trajectories observed at the same times.
Arguments
- data
The trajectories: a matrix or data frame with one trajectory per row and one time per column (or the transpose, see
byrow), or a list of trajectories (character vectors), possibly of different lengths.- byrow
Logical: for a matrix or data frame, is each trajectory a row (default) or a column?
- laplacian
Laplace smoothing: a constant added to every transition count before normalizing (default 0).
- name
Optional name of the fitted
markovchainList.
Value
A list with element estimate, the fitted
markovchainList; an empty list if no
transition can be counted.
Details
The \(k\)-th transition matrix is the maximum likelihood
estimate from the transitions observed between times \(k\) and
\(k + 1\) (columns \(k\) and \(k + 1\), or positions \(k\) and
\(k + 1\) of the trajectories long enough). Transitions with a missing
value (NA) are ignored, and pairs of times without any complete
transition are skipped.
See also
markovchainFit() for a homogeneous chain, rmarkovchain() to
simulate from the fit.
Examples
data(holson)
# a homogeneous chain for the whole panel
singleMc <- markovchainFit(data = holson[, 2:12])
# one transition matrix for each pair of consecutive years
mclistFit <- markovchainListFit(data = holson[, 2:12], name = "holsonMcList")
mclistFit$estimate
#> holsonMcList list of Markov chain(s)
#> Markovchain 1
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.94609164 0.05390836 0.0000000
#> 2 0.26356589 0.62790698 0.1085271
#> 3 0.02325581 0.18604651 0.7906977
#>
#> Markovchain 2
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9323410 0.0676590 0.0000000
#> 2 0.2551724 0.5103448 0.2344828
#> 3 0.0000000 0.0862069 0.9137931
#>
#> Markovchain 3
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.94765840 0.04820937 0.004132231
#> 2 0.26119403 0.66417910 0.074626866
#> 3 0.01428571 0.13571429 0.850000000
#>
#> Markovchain 4
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9172414 0.07724138 0.005517241
#> 2 0.1678322 0.60839161 0.223776224
#> 3 0.0000000 0.03030303 0.969696970
#>
#> Markovchain 5
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9579100 0.04208999 0.0000000
#> 2 0.1972789 0.70748299 0.0952381
#> 3 0.0000000 0.17073171 0.8292683
#>
#> Markovchain 6
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9462990 0.05224964 0.001451379
#> 2 0.1677019 0.61490683 0.217391304
#> 3 0.0000000 0.06666667 0.933333333
#>
#> Markovchain 7
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.949926362 0.04860088 0.001472754
#> 2 0.193103448 0.71034483 0.096551724
#> 3 0.005681818 0.15909091 0.835227273
#>
#> Markovchain 8
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.92581602 0.07418398 0.0000000
#> 2 0.06707317 0.73780488 0.1951220
#> 3 0.00000000 0.04320988 0.9567901
#>
#> Markovchain 9
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9637795 0.03622047 0.00000000
#> 2 0.2247191 0.70786517 0.06741573
#> 3 0.0000000 0.17647059 0.82352941
#>
#> Markovchain 10
#> Unnamed Markov chain
#> A 3 - dimensional discrete Markov Chain defined by the following states:
#> 1, 2, 3
#> The transition matrix (by rows) is defined as follows:
#> 1 2 3
#> 1 0.9585890 0.04141104 0.0000000
#> 2 0.1318681 0.74725275 0.1208791
#> 3 0.0000000 0.06626506 0.9337349
#>