depmix {depmixS4}R Documentation

Dependent Mixture Model Specifiction

Description

depmix creates an object of class depmix, a dependent mixture model, otherwise known as hidden Markov model. For a short description of the package see depmixS4.

Usage

        
        depmix(response, data=NULL, nstates, transition=~1, family=gaussian(), 
                prior=~1, initdata=NULL, respstart=NULL, trstart=NULL, instart=NULL,
                ntimes=NULL,...)        
        

Arguments

response The response to be modeled; either a formula or a list of formulae in the multivariate case; this interfaces to the glm distributions. See 'Details'.
data An optional data.frame to interpret the variables in the response and transition arguments.
nstates The number of states of the model.
transition A one-sided formula specifying the model for the transitions. See 'Details'.
family A family argument for the response. This must be a list of family's if the response is multivariate.
prior A one-sided formula specifying the density for the prior or initial state probabilities.
initdata An optional data.frame to interpret the variables occuring in prior. The number of rows of this data.frame must be equal to the number of cases being modeled. See 'Details'.
respstart Starting values for the parameters of the response models.
trstart Starting values for the parameters of the transition models.
instart Starting values for the parameters of the prior or initial state probability model.
ntimes A vector specifying the lengths of individual, ie independent, time series. If not specified, the responses are assumed to form a single time series. If the data argument has an attribute ntimes, then this is used.
... Not used currently.

Details

The function depmix creates an S4 object of class depmix, which needs to be fitted using fit to optimize the parameters.

The response model(s) are created by call(s) to response providing the response formula and the family specifying the error distribution. If response is a list of formulae, the response's are assumed to be independent conditional on the latent state.

The transitions are modeled as a multinomial logistic model for each state. Hence, the transition matrix can be modeled as time-dependent, depending on predictors. The prior density is also modeled as a multinomial logistic. Both are created by calls to transInit.

Starting values may be provided by the respective arguments. The order in which parameters must be provided can be easily studied by using the setpars function.

Linear constraints on parameters can be provided as argument to the fit function.

The print function prints the formulae for the response, transition and prior models along with their parameter values.

Value

depmix returns an object of class depmix which has the following slots:

response A list of a list of response models; the first index runs over states; the second index runs over the independent responses in case a multivariate response is provided.
transition A list of transInit models, ie multinomial logistic models with length the number of states.
prior A multinomial logistic model for the initial state probabilities.
dens,trDens,init See depmix-class help for details. For internal use.
stationary Logical indicating whether the transitions are time-dependent or not; for internal use.
ntimes A vector containing the lengths of independent time series; if data is provided, sum(ntimes) must be equal to nrow(data).
nstates The number of states of the model.
nresp The number of independent responses.
npars The total number of parameters of the model. Note: this is not the degrees of freedom because there are redundancies in the parameters, in particular in the multinomial models for the transitions and prior probabilities.

Author(s)

Ingmar Visser & Maarten Speekenbrink

References

On hidden Markov models: Lawrence R. Rabiner (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of IEEE, 77-2, p. 267-295.

On latent class models: A. L. McCutcheon (1987). Latent class analysis. Sage Publications.

See Also

fit, transInit, response, depmix-methods for accessor functions to depmix objects.

Examples


# create a 2 state model with one continuous and one binary response
data(speed)
mod <- depmix(list(rt~1,corr~1),data=speed,nstates=2,family=list(gaussian(),multinomial()))
# print the model, formulae and parameter values
mod


[Package depmixS4 version 0.2-1 Index]