sPhikf {mme}

Fisher information matrix and score vectors of the variance components for Model 1

Description

This function computes the Fisher information matrix and the score vectors of the variance components, for the multinomial mixed model with one independent random effect in each category of the response variable (Model 1). These values are used in the fitting algorithm implemented in modelfit1 to estimate the random effects. The algorithm adatps the ideas of Schall (1991) to a multivariate model. The variance components are estimated by the REML method.

Usage

sPhikf(pp, sigmap, X, eta, phi)

Arguments

pp

vector with the number of the auxiliary variables per category.

sigmap

a list with the model variance-covariance matrices for each domain obtained from wmatrix.

X

list of matrices with the auxiliary variables obtained from data.mme. The dimension of the list is the number of categories of the response variable minus one.

eta

matrix with the estimated log-rates of probabilities of each category over the reference category obtained from prmu.

phi

vector with the values of the variance components obtained from modelfit1.

Value

A list containing the following components.

S.k

phi score vector.

F

Fisher information matrix of the variance component phi.

References

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Multinomial-based small area estimation of labour force indicators. Statistical Modelling, 13 ,153-178.

Schall, R (1991). Estimation in generalized linear models with random effects. Biometrika, 78,719-727.

See Also

data.mme, initial.values, wmatrix, phi.mult, prmu, phi.direct, Fbetaf, ci, modelfit1, msef, mseb.

Examples

k=3 #number of categories of the response variable
pp=c(1,1) #vector with the number of auxiliary variables in each category
data(simdata) #data
mod=1 #type of model
datar=data.mme(simdata,k,pp, mod)
initial=datar$initial
mean=prmu(datar$n,datar$Xk,initial$beta.0,initial$u.0)
sigmap=wmatrix(datar$n,mean$estimated.probabilities)

##Fisher information matrix and score vectors
Fisher.phi=sPhikf(pp,sigmap,datar$X,mean$eta,initial$phi.0)