sPhikf.ct {mme}

Fisher information matrix and score vectors of the variance components for Model 3

Description

This function computes the Fisher information matrix and the score vectors of the variance components, for the multinomial mixed model with two independent random effects for each category of the response variable: one domain random effect and another correlated time and domain random effect (Model 3). These values are used in the fitting algorithm implemented in modelfit3 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.ct(d, t, pp, sigmap, X, eta, phi1, phi2, rho, pr, M)

Arguments

d

number of areas.

t

number of time periods.

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 probabilites of each category over the reference category obtained from prmu.time.

phi1

vector with the values of the first variance component obtained from modelfit3.

phi2

vector with the values of the second variance component obtained from modelfit3.

rho

vector with the correlation parameter obtained from modelfit3.

pr

matrix with the estimated probabilities of the response variable obtained from prmu.time.

M

vector with the area sample sizes.

Value

A list containing the following components.

S

(phi1, phi2, rho) score vector.

F

Fisher information matrix of the variance components (phi1, phi2, rho).

References

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Small area estimation of labour force indicators under a multinomial mixed model with correlated time and area effects. Submitted for review.

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

See Also

data.mme, initial.values, wmatrix, phi.mult.ct, prmu.time, phi.direct.ct, Fbetaf.ct, omega, ci, modelfit3, msef.ct, 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
mod=3 #type of model
data(simdata3) #data
datar=data.mme(simdata3,k,pp, mod)
initial=datar$initial
mean=prmu.time(datar$n,datar$Xk,initial$beta.0,initial$u1.0,initial$u2.0)
sigmap=wmatrix(datar$n,mean$estimated.probabilities)

## Fisher information matrix and the score vectors
Fisher.phi.ct=sPhikf.ct(datar$d,datar$t,pp,sigmap,datar$X,mean$eta,initial$phi1.0,
           initial$phi2.0,initial$rho.0,mean$estimated.probabilities,datar$n)