MissMech (version 1.0.4)

Mls: ML Estimates of Mean and Covariance Based on Incomplete Data

Description

Normal theory maximum likelihood estimates of mean and covariance matrix is obtained when data are incomplete, using EM algorithm (see Jamshidian and Bentler 1999). If the option Hessian is set to TRUE, then the observed information containing the standard errors of the parameter estimates is also computed.

Usage

Mls(data, mu = NA, sig = NA, tol = 1e-06, Hessian = FALSE)

Value

mu

The maximum likelihood estimate of the mean vector.

sig

The maximum likelihood estimates of the covariance matrix.

hessian

The Hessian of the observed data log-likelihood function.

stderror

The negative of the inverse of the Hessian of the observed data log-likelihood function. The diagonal elements of stderror are the variance of the parameters based on the observed informaion matrix.

iteration

The number of iterations used in the EM iterative process.

Arguments

data

A matrix consisting of at least two columns. Values must be numerical with missing data indicated by NA.

mu

EM iteration initial value for mu (the mean vector). The default is a zero vector.

sig

EM iteration initial value for sigma (the covariance matrix). The default is the identity matrix.

tol

The tolerance value used in the convergence criteria described in Jamshidian and Bentler (1999) for stopping the EM algorithm.

Hessian

Hessian of the log-likelihood function, see Jamshidian and Bentler (1999).

Author

Mortaza Jamshidian, Siavash Jalal, and Camden Jansen

References

Jamshidian, M. and Bentler, P. M. (1999). ``ML estimation of mean and covariance structures with missing data using complete data routines.'' Journal of Educational and Behavioral Statistics, 24, 21-41, tools:::Rd_expr_doi("10.2307/1165260").

Examples

set.seed <- 50
n <- 200
p <- 4
pctmiss <- 0.2 # Generate 20\% missing data
y <- matrix(rnorm(n * p),nrow = n)
missing <- matrix(runif(n * p), nrow = n) < pctmiss
y[missing] <- NA
ml <- Mls(data=y, mu = NA, sig = NA, tol = 1e-6, Hessian=FALSE)
ml