hmmm (version 1.0.0)

hidden.emfit: ML estimation of a multinomial hidden Markov model

Description

Maximum likelihood estimation of a hidden Markov model with several observed categorical variables. Observed and latent processes are specified by hmm models.

Usage

hidden.emfit(y, model.obs, model.lat, noineq = TRUE, maxit = 10, maxiter = 100, 
norm.diff.conv = 1e-05, norm.score.conv = 1e-05, y.eps = 0, mup = 1, step = 1, 
printflag = 0, old.tran.p = NULL, bb = NULL)

Arguments

y

The observed multivariate categorical time series

model.obs

The model for the observations specified by `hmmm.model'

model.lat

The model for the latent chain specified by `hmmm.model'

noineq

If TRUE inequality constraints are not used

maxit

Maximum number of iterations for the M step

maxiter

Maximum number of iterations for the EM algorithm

norm.diff.conv

Convergence criterium for the parameters

norm.score.conv

Convergence criterium for the log-likelihood function

y.eps

Non-negative constant to be added to the original counts in y

mup

Weight for the constraints penalty part of the merit function

step

Interval length for the line search

printflag

If printflag=n the log-likelihood function is displayed at any n iterations

old.tran.p

Starting values for the transition matrix

bb

Starting values for the observation probabilities

Value

• vecpar
  List of two vectors of parameters of the observed and latent processes
• initial
  Invariant distribution of the latent process
• Ptr
  Estimated transition probabilities
• Ptobs
  Estimated observation probabilities
• Ptr.iniz
  Starting values of Ptr
• Ptobs.iniz
  Starting values for Ptobs
• filter
  Filtered probabilities
• smooth
  Smoothed probabilities
• conv
  List of convergence criteria

Details

The model for the transition matrix of the latent Markov chain and the model for the multinomial process are marginal models specified by `hmmm.model'. In defining the hmm model for the observations, variable 1 indicates the latent variable and its logits must not be constrained. In the model for the latent variable, 2 is the variable at time (t-1) and 1 the variable at time t. Logits of variable 2 must not be constrained.

References

Colombi R, Giordano S (2011) Lumpability for discrete hidden Markov models. Advances in Statistical Analysis, 95(3), 293-311.

See Also

print.hidden, {summary.hidden}

Examples

data(drinks)
y<-cbind(drinks$lemon.tea,drinks$orange.juice)
fm<-c("l-l-l")
fmargobs<-marg.list(fm,mflag="m")
#initial values of transition matrix and obs distribution given the two latent states
Ptr<-matrix(c(0.941, 0.199,0.059, 0.801),2,2,byrow=TRUE)
Ptobs<-matrix(c(0.053, 0.215, 0.206, 0.001, 0.039, 0.021, 0.020, 0.176, 0.270,
                0.000, 0.000, 0.000, 0.048, 0.263, 0.360, 0.065, 0.053, 0.211),
2,9,byrow=TRUE)
find<-~lat+lat*tea+lat*juice   # lat is the latent variable
model.obsf<-hmmm.model(marg=fmargobs,
lev=c(2,3,3),names=c("lat","tea","juice"),formula=find)

# model of independent observed variables given the latent states
modelind<-hidden.emfit(y,model.obsf,y.eps=0.01,maxit=10,maxiter=2500,
old.tran.p=Ptr,bb=Ptobs)
print(modelind,printflag=TRUE)