clickb (version 0.1)

fit_mixmar: Bayesian estimation for mixture of Markov models with fixed number of components

Description

The function use a sampling algorithm for estimating bayesian mixture of Markov models with fixed number of components. If simulated data are used, quality of classification is assessed comparing the original partition of the sequences with the one identified by the algorithm through Danon similarity and adjusted Rand indices.

Usage

fit_mixmar(
  data,
  iter = 1000,
  burn = 500,
  num.cluster,
  states,
  A.ini = NULL,
  pi.ini = NULL,
  prior.ini = 1,
  prior.transrow = 1,
  prior.mixcoef = 1,
  ini.constr = NULL,
  trans.constr = NULL
)

Value

pi.list

Initial Markov chain probabilities for MCMC

A.list

Transition Markov chain probabilities for MCMC

Sim.index.Danon

Danon similarity between two partitions

Sim.index.Rand

Rand similarity between two partitions

Conf.mat

Confusion matrix between two partitions

Arguments

data

are dataset containing a variable for categorical observations and an ID variable to identify subjects. No missing values allowed

iter

is the number of iterations

burn

is the number of burn-in iterations

num.cluster

is the number of clusters

states

is the number of states of the Markov chain

A.ini

is the list of initial values for the transition matrices

pi.ini

is the list of initial values for the initial probability vectors

prior.ini

is the hyperparameter for the prior distribution of initial probability vector (Dirichlet)

prior.transrow

is the hyperparameter for the prior distribution of transition matrices rows (Dirichlet)

prior.mixcoef

is the hyperparameter for the prior distribution of mixture coefficients (Dirichlet)

ini.constr

is the vector of zeros and ones indicating constrains in initial probabilities (zero: not possible to start from that state)

trans.constr

is the matrix of zeros and ones indicating constrains in transition probabilities (zero: transition is not allowed)

Author

Furio Urso

Examples

# \donttest{
#Compare model-based clustering with respect to another classification

# Set up initial values and hyper parameters (either fixed or random)

iter<-5   # number of iterations for the Gibbs sampler
burn<-0

num.cluster <- 3 # number of components
states <- 5 # number of states

ini.constr<-c(1, 0, 1, 1, 1)           # constrains on initial probabilities               
trans.constr<-matrix(c(1, 1, 1, 0, 1,  # constrains on transition probabilities                   
             1, 0, 1, 1, 1,                                  
             1, 1, 1, 1, 0,                                 
             0, 1, 1, 1, 1,                                 
             1, 1, 0, 1, 1),byrow=TRUE,nrow=5) 

# parameters initial values
A.ini <- 1/states*matrix(rep(1, length = (states^2)), 
                         nrow = states, byrow = TRUE, 
                         dimnames = list(as.character(c(1:states))) )
pi.ini <- rep(1/states, length = states)

# Prior distributions' hyperparameters
prior.ini<- prior.transrow <- prior.mixcoef <- 1  

# data is the simulated sequential dataset obtained in the sim_seq() example

# Run the MCMC to estimate parameters 
MMM_1 <- fit_mixmar(data, iter, burn, num.cluster = num.cluster, states = states,
                     A.ini = A.ini, pi.ini = pi.ini, prior.ini = prior.ini, 
                     prior.transrow = prior.transrow, prior.mixcoef = prior.mixcoef, 
                     ini.constr = ini.constr, trans.constr = trans.constr)

 # }