# Computes Group Sizes, Group Membership and Individual Posterior Classification Probabilities

### Description

Computes (estimates) group sizes, group membership and individual posterior classification probabilities based on the outcome of a specificed MCMC run of either mcClust, mcClustExtended, dmClust or dmClustExtended as well as MNLAuxMix.

### Usage

  1 2 3 4 5 6 7 8 9 10 calcAllocationsMCC(outList, thin = 1, maxi = 50, M0 = outList$Mcmc$M0, plotPathsForEta = TRUE) calcAllocationsMCCExt(outList, thin = 1, maxi = 50, M0 = outList$Mcmc$M0) calcAllocationsDMC(outList, thin = 1, maxi = 50, M0 = outList$Mcmc$M0, plotPathsForEta = TRUE) calcAllocationsDMCExt(outList, thin = 1, maxi = 50, M0 = outList$Mcmc$M0) calcAllocationsMNL(outList, thin = 1, maxi = 50, M0 = outList$Mcmc$M0) 

### Arguments

 outList specifies a list containing the outcome (return value) of an MCMC run of mcClust, dmClust, mcClustExtended, dmClustExtended or MNLAuxMix. 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), except for mixing proportions/weights η where all thin-th draws beginning at M0 are used. M0 specifies the number of the first MCMC draw after burn-in (default is outList$Mcmc$M0). plotPathsForEta If TRUE (default) paths of the MCMC draws of the mixing proportions/weights η (corresponding to group sizes) are drawn.

### Details

The last maxi MCMC draws of each thin-th draw are taken for calculations, except for mixing proportions η (which are part of MCC and DMC without MNL extension) where all thin-th draws beginning at M0 are used.

### Value

A list containing:

 estGroupSize  A vector of dimension H containing the posterior mean of group sizes. For MCC and DMC without MNL extension estGroupSize contains the mixing proportions/weights \hat{η}. In these cases each thin-th MCMC draw beginning at M0 (after burn-in) is used for calculation. For MCC and DMC with MNL extension and MNLAuxMix the group sizes are calculated based on the individual posterior classification probabilities which are calculated using the last maxi draws of each thin-th MCMC draw. class  A vector of length N containing the group membership, which is determined for each individual according to the maximum individual posterior classification probability. classProbs  A matrix with dimension N x H containing the individual posterior classification probabilities which are calculated using the last maxi draws of each thin-th MCMC draw.

### Note

The last maxi MCMC draws of each thin-th draw are taken for calculations, except for mixing proportions η (which are part of MCC and DMC without MNL extension) where all thin-th draws beginning at M0 are used.

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

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