hmmm (version 1.0-4)

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

Description

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

Usage

hidden.emfit(y, model.obs, model.lat, nlat = 1, 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, q.par=1)

Arguments

y

The observed multivariate categorical time series

model.obs

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

model.lat

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

nlat

The number of latent variables

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 any n iterations

old.tran.p

Starting values for the transition matrix

bb

Starting values for the observation probabilities

q.par

The percentage of parameters that must satisfy the convergence criterium, q.par has values in [0 1]

Value

vecpar

List of two vectors of parameters of the observed and latent processes

model.obs

Information about the observed process

model.lat

Information about the latent process

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.

Use `print' or `summary' to display the output.

Details

Every column of y corresponds to an observed variable, every row in y reports the realization of the observed variable at each time occasion. The r realizations of each observed variable must be coded by the first r integers. The model.lat and model.obs are objects inheriting from class hmmmmod. So, the model for the transition matrix of the latent Markov chain and the model for the multinomial process can be marginal models specified by `hmmm.model' or `hmmm.model.X'. Consider a hidden Markov model for p observed variables and q latent variables. In defining the hmm models for observed and latent components using `hmmm.model' bear in mind that: for the observations, the first q variables are the latent variables, followed by the p observed variables; in the latent model, the first q variables refer to the latent at time t, while the remaining q indicate the latent variables at time (t-1). Note that in both cases the first marginal set must contain only the latent variables. On the other hand, in defining the hmm models for the observations and latent chain using `hmmm.model.X' consider that: for the observed model, the responses are the observed variables while the latent variables have the role of covariates and the number of their categories is declared in strata; in the latent model, the responses are the latent variables at time t, while the lagged variables at time (t-1) are considered as covariates. Declare the argument nlat only if model.obs is specified by `hmmm.model' and model.lat is not explicitly defined.

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, hmmm.model, hmmm.model.X

Examples

# NOT RUN {
data(drinks)
y<-cbind(drinks$lemon.tea,drinks$orange.juice)
fm<-c("l-l-l")
fmargobs<-marg.list(fm)
#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)

#alternative definition based on hmmm.model.X
f<-list(tea=~tea*lat,juice=~juice*lat,tea.juice="zero")
model.obsfX<-hmmm.model.X(marg=marg.list(c("l-l")),names=c("tea","juice"),
fnames=c("lat"),lev=c(3,3),strata=c(2))
modelindX<-hidden.emfit(y,model.obsfX,y.eps=0.01,maxit=10,maxiter=2500,
old.tran.p=Ptr,bb=Ptobs)
modelindX
summary(modelindX)
# }