estim {mmeln}

Maximum Likelihood estimation of the model parameters

Description

Compute the MLE of the model parameters using the E-M (Expectation-Maximization) algorithm

Usage

## S3 method for class 'mmeln'
estim(X,...,mu=NULL,tau=NULL,sigma=NULL,random.start=FALSE,iterlim=500,tol=1e-8)

Arguments

X

An object of type mmeln containing the design of the model, see mmeln

...

For the moments no other arguments can be added

mu

A list of length X$G containing the starting value for the location parameters

tau

The starting value for the mixture parameters

sigma

A list of length X$G containing the starting value for the covariances parameters

random.start

A True/False value indicating if the starting parameters should be given at random. If true the starting values are not needed.

iterlim

The maximum number of iterations allowed

tol

Tolerance, degree of precision required to stop the iterative process

Details

Methods estim.mmeln... are used by the estim function but are of no use outside this method.

Value

Retourne un objet de type "mmeln" & "mmelnSOL" les arguments suivants :

obj$Y

The data matrix

obj$G

The number of groups

obj$p

Number of column in Y

obj$N

Number of row in Y

obj$Xg

The list of location design matrices

obj$pl

The number of location parameters

obj$Z

Mixture design matrix

obj$pm

The number of mixture parameters

obj$cov

Covariance type

obj$equalcov

logical value indicating if covariance is equal across group

obj$pc

The number of covariance parameters

Author(s)

Charles-Édouard Giguère

References

McLachlan, G. & Peel, D. (2000), Finite mixture models,Wiley

Flury, B. D. (1997), A first course in multivariate statistics, Springer

Pinheiro J. C. and Bates D. M. (2000), Mixed-Effects Models in S and S-PLUS, Springer

Srivastava, M.S. (2002), Methods of Multivariate Statistics, WILEY

Lindstrom M. J. and Bates D. M. (1988), Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-MeasuresData, Journal of the American Statistical Association,American Statistical Association,V. 83,I. 404, P. 1014-1022

See Also

mmeln.package

Examples

data(exY)
### estimation of the parameters of the mixture
temps=0:2
mmeln1=mmeln(Y, G = 3, form.loc = list(~temps, ~temps + I(temps^2),
                       ~temps + I(temps^2)), form.mel = ~SEXE, cov = "CS")
mmelnSOL1=estim(mmeln1,mu = list(c(1,1), c(2,0,0), c(3,0,0)),
    tau = c(0,0,0,0), sigma = list(c(1,0), c(1,0), c(1,0)))