Revision 1c995ef374a8438306839bffe3c09b7c524aebdd authored by Derek Young on 28 April 2009, 07:56:28 UTC, committed by cran-robot on 28 April 2009, 07:56:28 UTC
1 parent cda9e55
regmixEM.mixed.Rd
\name{regmixEM.mixed}
\title{EM Algorithm for Mixtures of Regressions with Random Effects}
\alias{regmixEM.mixed}
\usage{
regmixEM.mixed(y, x, w = NULL, sigma = NULL, arb.sigma = TRUE,
alpha = NULL, lambda = NULL, mu = NULL,
rho = NULL, R = NULL, arb.R = TRUE, k = 2,
ar.1 = FALSE, addintercept.fixed = FALSE,
addintercept.random = TRUE, epsilon = 1e-08,
maxit = 10000, verb = FALSE)
}
\description{
Returns EM algorithm output for mixtures of multiple regressions with random effects
and an option to incorporate fixed effects and/or AR(1) errors.
}
\arguments{
\item{y}{A list of N response trajectories with (possibly) varying dimensions of
length \eqn{n_i}.}
\item{x}{A list of N design matrices of dimensions \eqn{(n_i)\times p}{(n_i) x p}.
Each trajectory in y has
its own design matrix.}
\item{w}{A list of N known explanatory variables having dimensions \eqn{(n_i)\times q}{(n-1) x q}.
If \code{mixed} = FALSE,
then \code{w} is replaced by a list of N zeros.}
\item{sigma}{A vector of standard deviations. If NULL, then \eqn{1/s^2} has
random standard exponential entries according to a binning method done on the data.}
\item{arb.sigma}{If TRUE, then \code{sigma} is k-dimensional. Else a common standard deviation is assumed.}
\item{alpha}{A q-vector of unknown regression parameters for the fixed effects. If NULL and \code{mixed} = TRUE, then \code{alpha} is
random from a normal distribution with mean and variance according to a binning method done
on the data. If \code{mixed} = FALSE, then \code{alpha} = 0.}
\item{lambda}{Initial value of mixing proportions for the assumed mixture structure on the regression coefficients.
Entries should sum to 1. This determines number of components. If NULL, then \code{lambda} is
random from uniform Dirichlet and the number of components is determined by \code{mu}.}
\item{mu}{A pxk matrix of the mean for the mixture components of the random regression coefficients. If NULL, then the columns
of \code{mu} are random from a multivariate normal distribution with mean and variance determined by a binning method
done on the data.}
\item{rho}{An Nxk matrix giving initial values for the correlation term in an AR(1) process. If NULL, then these values
are simulated from a uniform distribution on the interval (-1, 1).}
\item{R}{A list of N pxp covariance matrices for the mixture components of the random regression coefficients. If NULL, then
each matrix is random from a standard Wishart distribution according to a binning method done on the data.}
\item{arb.R}{If TRUE, then \code{R} is a list of N pxp covariance matrices. Else, one common covariance matrix is assumed.}
\item{k}{Number of components. Ignored unless \code{lambda} is NULL.}
\item{ar.1}{If TRUE, then an AR(1) process on the error terms is included. The default is FALSE.}
\item{addintercept.fixed}{If TRUE, a column of ones is appended to the matrices in w.}
\item{addintercept.random}{If TRUE, a column of ones is appended to the matrices in x before p is calculated.}
\item{epsilon}{The convergence criterion.}
\item{maxit}{The maximum number of iterations.}
\item{verb}{If TRUE, then various updates are printed during each iteration of the algorithm.}
}
\value{
\code{regmixEM} returns a list of class \code{mixEM} with items:
\item{x}{The predictor values corresponding to the random effects.}
\item{y}{The response values.}
\item{w}{The predictor values corresponding to the (optional) fixed effects.}
\item{lambda}{The final mixing proportions.}
\item{mu}{The final mean vectors.}
\item{R}{The final covariance matrices.}
\item{sigma}{The final component error standard deviations.}
\item{alpha}{The final regression coefficients for the fixed effects.}
\item{rho}{The final error correlation values if an AR(1) process is included.}
\item{loglik}{The final log-likelihood.}
\item{posterior.z}{An Nxk matrix of posterior membership probabilities.}
\item{posterior.beta}{A list of N pxk matrices giving the posterior regression coefficient values.}
\item{all.loglik}{A vector of each iteration's log-likelihood.}
\item{restarts}{The number of times the algorithm restarted due to unacceptable choice of initial values.}
\item{ft}{A character vector giving the name of the function.}
}
\seealso{
\code{\link{regmixEM}}, \code{\link{post.beta}}
}
\references{
Xu, W. and Hedeker, D. (2001) A Random-Effects Mixture Model for Classifying Treatment Response in
Longitudinal Clinical Trials, \emph{Journal of Biopharmaceutical Statistics}, \bold{11(4)}, 253--273.
}
\examples{
## EM output for simulated data from 2-component mixture of random effects.
data(RanEffdata)
x<-lapply(1:length(RanEffdata), function(i)
matrix(RanEffdata[[i]][, 2:3], ncol = 2))
x<-x[1:20]
y<-lapply(1:length(RanEffdata), function(i)
matrix(RanEffdata[[i]][, 1], ncol = 1))
y<-y[1:20]
lambda<-c(0.45, 0.55)
mu<-matrix(c(0, 4, 100, 12), 2, 2)
sigma<-2
R<-list(diag(1, 2), diag(1, 2))
em.out<-regmixEM.mixed(y, x, sigma = sigma, arb.sigma = FALSE,
lambda = lambda, mu = mu, R = R,
addintercept.random = FALSE,
epsilon = 1e-02, verb = TRUE)
em.out[4:10]
}
\keyword{file}
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