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\name{pnext.msm}
\alias{pnext.msm}
\title{Probability of each state being next}
\description{
Compute a matrix of the probability of each state \eqn{s} being the
next state of the process after each state \eqn{r}. Together with
the mean sojourn times in each state (\code{\link{sojourn.msm}}),
these fully define a continuous-time Markov model.
}
\usage{
pnext.msm(x, covariates = "mean",
ci=c("delta","normal","bootstrap","none"), cl = 0.95, B=1000)
}
\arguments{
\item{x}{A fitted multi-state model, as returned by
\code{\link{msm}}.}
\item{covariates}{
The covariate values at which to estimate the intensities.
This can either be:\cr
the string \code{"mean"}, denoting the means of the covariates in
the data (this is the default),\cr
the number \code{0}, indicating that all the covariates should be
set to zero,\cr
or a list of values, with optional names. For example
\code{list (60, 1)}
where the order of the list follows the order of the covariates
originally given in the model formula, or a named list,
\code{list (age = 60, sex = 1)}
}
\item{ci}{
If \code{"delta"} (the default) then confidence intervals are
calculated by the delta method.
If \code{"normal"}, then calculate a confidence interval by
simulating \code{B} random vectors
from the asymptotic multivariate normal distribution implied by the
maximum likelihood estimates (and covariance matrix) of the log
transition intensities and covariate effects, then transforming.
If \code{"bootstrap"} then calculate a confidence interval by
non-parametric bootstrap refitting. This is 1-2 orders of magnitude
slower than the \code{"normal"} method, but is expected to be more
accurate. See \code{\link{boot.msm}} for more details of
bootstrapping in \pkg{msm}.}
\item{cl}{Width of the symmetric confidence interval to present.
Defaults to 0.95.}
\item{B}{Number of bootstrap replicates, or number of normal
simulations from the distribution of the MLEs.}
}
\value{
The matrix of probabilities that the next move of a process in state
\eqn{r} (rows) is to state \eqn{s} (columns).
}
\details{
For a continuous-time Markov process in state \eqn{r}, the probability
that the next state is \eqn{s} is \eqn{-q_{rs} / q_{rr}}, where
\eqn{q_{rs}} is the transition intensity (\code{\link{qmatrix.msm}}).
The model is fully parameterised by these probabilities together with
the mean sojourn times \eqn{-1/q_{rr}} in each state \eqn{r}. This
gives a more intuitively meaningful description of a model than the
intensity matrix.
Remember that \pkg{msm} deals with continuous-time not discrete-time
models, so these are \emph{not} the same as the probability of observing
state \eqn{s} at a fixed time in the future. Those probabilities are
given by \code{\link{pmatrix.msm}}.
}
\seealso{
\code{\link{qmatrix.msm}},\code{\link{pmatrix.msm}},\code{\link{qratio.msm}}
}
\author{C. H. Jackson \email{chris.jackson@mrc-bsu.cam.ac.uk}}
\keyword{models}
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