EM_REML_MM {KRMM}

Expectation-Maximization (EM) algorithm for the restricted maximum likelihood (REML) associated to the mixed model

Description

EM_REML_MM estimates the components and variance parameters of the following mixed model; Y =X*Beta + Z*U + E, using the EM-REML algorithm.

Usage

		EM_REML_MM( Mat_K_inv, Y, X, Z, init_sigma2K, 
		
		init_sigma2E, convergence_precision, 
		
		nb_iter, display )		
	

Arguments

Mat_K_inv

numeric matrix; the inverse of the kernel matrix

Y

numeric vector; response vector

X

numeric matrix; design matrix of predictors with fixed effects

Z

numeric matrix; design matrix of predictors with random effects

init_sigma2K, init_sigma2E

numeric scalars; initial guess values, associated to the mixed model variance parameters, for the EM-REML algorithm

convergence_precision, nb_iter

convergence precision (i.e. tolerance) associated to the mixed model variance parameters, for the EM-REML algorithm, and number of maximum iterations allowed if convergence is not reached

display

boolean (TRUE or FALSE character string); should estimated components be displayed at each iteration

Value

Beta_hat

Estimated fixed effect(s)

Sigma2K_hat, Sigma2E_hat

Estimated variance components

Author(s)

Laval Jacquin <[e-mail]>

References

Foulley, J.-L. (2002). Algorithme em: théorie et application au modèle mixte. Journal de la Société française de Statistique 143, 57-109