# Calculates And Plots the Long-Run Distribution Over the Categories of the Outcome Variable After Certain Periods.

### Description

Calculates and plots the posterior expectation of the cluster-specific 'long-run' distribution over the categories
of the outcome variable after a period of certain time units *t* in the various clusters starting at a specified
initial state vector (corresponding to *t=0*). The calculation is based on the transition matrices for each
cluster/group. It includes also the stationary distribution (*t=Inf*).

### Usage

1 2 3 4 | ```
calcLongRunDist(outList, initialStateData, class, equiDist,
thin = 1, maxi = 50, M0 = outList$Mcmc$M0,
printLongRunDist = TRUE,
grLabels = paste("Group", 1:outList$Prior$H) )
``` |

### Arguments

`outList` |
specifies a list containing the outcome (return value) of an MCMC run of |

`initialStateData` |
A vector of length |

`class` |
A vector of length |

`equiDist` |
A matrix of dimension |

`thin` |
An integer specifying the thinning parameter (default is 1). |

`maxi` |
specifies the number of draws to be actually taken (after thinning) from the MCMC draws beginning from the end of the chain (default is 50). |

`M0` |
specifies the number of the first MCMC draw after burn-in (default is |

`printLongRunDist` |
If |

`grLabels` |
A character vector giving user-specified names for the clusters/groups. |

### Details

A barplot of the long-run distributions is drawn for each cluster/group, including also the stationary distribution (steady state).

The last `maxi`

MCMC draws of each `thin`

-th draw are taken for calculations.

### Value

A list containing the long-run distributions for each cluster/group.

### Note

Note, that in contrast to the literature (see **References**), the numbering (labelling) of the states of the
categorical outcome variable (time series) in this package is sometimes *0,...,K* (instead of
*1,...,K*), however, there are *K+1* categories (states)!

### Author(s)

Christoph Pamminger <christoph.pamminger@gmail.com>

### References

Sylvia Fruehwirth-Schnatter, Christoph Pamminger, Andrea Weber and Rudolf Winter-Ebmer, (2011),
"Labor market entry and earnings dynamics: Bayesian inference using
mixtures-of-experts Markov chain clustering".
*Journal of Applied Econometrics*. DOI: 10.1002/jae.1249
http://onlinelibrary.wiley.com/doi/10.1002/jae.1249/abstract

Christoph Pamminger and Sylvia Fruehwirth-Schnatter, (2010),
"Model-based Clustering of Categorical Time Series".
*Bayesian Analysis*, Vol. 5, No. 2, pp. 345-368. DOI: 10.1214/10-BA606
http://ba.stat.cmu.edu/journal/2010/vol05/issue02/pamminger.pdf

### See Also

`calcAllocations`

, `calcEquiDist`

, `mcClust`

, `dmClust`

, `mcClustExtended`

,
`dmClustExtended`

, `barplot2 `

### Examples

1 2 | ```
# please run the examples in mcClust, dmClust, mcClustExtended,
# dmClustExtended
``` |