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# View of /trunk/man/depmix.Rd

Fri Mar 7 16:16:50 2008 UTC (11 years, 8 months ago) by ingmarvisser
File size: 6252 byte(s)
Updated help files and other minor changes
\name{depmix}

\alias{depmix}
\alias{logLik}
\alias{logLik,depmix-method}
\alias{AIC}
\alias{AIC,depmix-method}
\alias{BIC}
\alias{BIC,depmix-method}

\alias{npar}
\alias{npar,depmix-method}

\alias{freepars}
\alias{freepars,depmix-method}

\alias{setpars}
\alias{setpars,depmix-method}

\alias{getpars}
\alias{getpars,depmix-method}

\title{Dependent Mixture Model Specifiction}

\description{

\item{depmix}{\code{depmix} creates an object of class \code{depmix}, a
dependent mixture model, or hidden Markov model.}

}
\usage{

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

\S4method{logLik}{depmix}(object)
\S4method{AIC}{depmix}(object)
\S4method{BIC}{depmix}(object)
\S4method{freepars}{depmix}(object)
\S4method{npar}{depmix}(object)
\S4method{freepars}{depmix}(object)
\S4method{setpars}{depmix}(object,which="pars",...)
\S4method{getpars}{depmix}(object,which="pars",...)

}
\arguments{
\item{object}{An object with class \code{depmix}.}

\item{response}{The response to be modeled; either a formula or a list
of formulae in the multivariate case. See details.}

\item{data}{An optional data.frame to interpret the variables in
response and transition.}

\item{nstates}{The number of states of the model.}

\item{transition}{A one-sided formula specifying the model for the
transitions. See details.}

\item{family}{A family argument for the response. This must be a list
of family's if the response is multivariate.}

\item{prior}{A one-sided formula specifying the density for the prior
or initial state probabilities.}

\item{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.}

\item{respstart}{Starting values for the parameters of the response
models.}

\item{trstart}{Starting values for the parameters of the transition
models.}

\item{instart}{Starting values for the parameters of the prior or
initial state probability model.}

\item{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.}

\item{which}{The default "pars" returns a vector of all parameters of a
\code{depmix} object; the alternative value "fixed" return a
logical vector of the same length indicating which parameters are
fixed. The setpars functions sets parameters (or the logical fixed
vector) to new values; \code{setpars} also recomputes the dens,
trans and init slots of \code{depmix} objects. Note that the
\code{getpars} and \code{setpars} functions for \code{depmix}
objects simply call the functions of the same name for the response
and transition models.}

\item{...}{Not used currently.}

}

\details{

The function \code{depmix} creates an S4 object of class \code{depmix},
which needs to be fitted using \code{\link[depmix]{depmix.fit}} to
optimize the parameters.

The response model(s) are created by call(s) to
\code{\link[depmix]{response}} providing the family and optional
predictors.  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

Starting values may be provided by the respective arguments.  The order
in which parameters must be provided can be easily studied by using the
\code{setpars} function (see example).

Linear constraints on parameters can be provided as argument to the

}
\value{

\code{depmix} returns an object of class \code{depmix} which has print and
summary methods. It has the following slots:

\item{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.}

\item{transition}{A list of \code{transInit} models, ie multinomial
logistic models with length the number of states.}

\item{prior}{A multinomial logistic model for the initial state
probabilities.}

\item{dens,trDens,init}{See depmix-class help for details. For internal
use.}

\item{stationary}{Logical indicating whether the transitions are
time-dependent or not; for internal use.}

\item{ntimes}{A vector containing the lengths of independent time
series; if data is provided, sum(ntimes) must be equal to
nrow(data).}

\item{nstates}{The number of states of the model.}

\item{nresp}{The number of independent responses.}

\item{npars}{The total number of parameters of the model. This is not
the degrees of freedom, ie there are redundancies in the
parameters, in particular in the multinomial models for the
transitions and prior.}

\code{logLik}, \code{AIC}, and \code{BIC} return the respective associated
with the current parameter values.  \code{nobs} returns the number of
observations, ie \code{sum(ntimes)} that is used in computing the
\code{BIC}.  \code{npar} returns the number of paramters of a model;
\code{freepars} returns the number of non-fixed parameters.

}

\author{Ingmar Visser \email{i.visser@uva.nl}}

\seealso{
}

\references{

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

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

}

\examples{

# create a 2 state model with one continuous and one binary response
data(speed)
depmix(list(rt~1,corr~1),data=speed,nstates=2,family=list(gaussian(),multinomial()))

}
\keyword{models}