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

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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

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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 mcClust, dmClust, mcClustExtended or dmClustExtended.

initialStateData

A vector of length N containing the initial states where to start from.

class

A vector of length N containing the group membership returned by calcAllocations.

equiDist

A matrix of dimension (K+1) x H containing the stationary distributions (steady states) of the Markov chains (outcome variable) in the various clusters returned by calcEquiDist.

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 outList$Mcmc$M0).

printLongRunDist

If TRUE (default) a LaTeX-style table containing the long-run distribution for each cluster/group is generated.

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

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# please run the examples in mcClust, dmClust, mcClustExtended, 
# dmClustExtended

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