Finds the maximum likelihood estimates of the mean vector and
variance-covariance matrix for multivariate normal data with
(potentially) missing values.
Usage
mlest(data, ...)
Arguments
data
A data frame or matrix containing multivariate normal
data. Each row should correspond to an observation, and each
column to a component of the multivariate vector. Missing values
should be coded by 'NA'.
...
Optional arguments to be passed to the nlm optimization routine.
Details
The estimate of the variance-covariance matrix returned by
mlest is necessarily positive semi-definite. Internally,
nlm is used to minimize the negative log-likelihood, so
optional arguments mayh be passed to nlm which modify the
details of the minimization algorithm, such as iterlim. The
likelihood is specified in terms of the inverse of the Cholesky factor
of the variance-covariance matrix (see Pinheiro and Bates 2000).
mlest cannot handle data matrices with more than 50 variables.
Each varaible must also be observed at least once.
Value
muhat
MLE of the mean vector.
sigmahat
MLE of the variance-covariance matrix.
value
The objective function that is minimized by nlm.
Is is proportional to twice the negative log-likelihood.
gradient
The curvature of the likelihood surface at the MLE, in
the parameterization used internally by the optimization
algorithm. This parameterization is: mean vector first, followed
by the log of the diagonal elements of the inverse of the Cholesky
factor, and then the elements of the inverse of the Cholesky
factor above the main diagonal. These off-diagonal elements are
ordered by column (left to right), and then by row within column
(top to bottom).
stop.code
The stop code returned by nlm.
iterations
The number of iterations used by nlm.
References
Little, R. J. A., and Rubin, D. B. (1987) Statistical Analysis
with Missing Data. New York: Wiley.
Pinheiro, J. C., and Bates, D. M. (1996) Unconstrained
parametrizations for variance-covariance matrices.
Statistics and Computing6, 289–296.
Pinheiro, J. C., and Bates, D. M. (2000) Mixed-effects models in
S and S-PLUS. New York: Springer.