phi.direct.ct {mme}

Variance components for Model 3

Description

This function calculates 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). This variance components are used in the second part of the fitting algorithm implemented in modelfit3. The algorithm adapts the ideas of Schall (1991) to a multivariate model. The variance components are estimated by the REML method.

Usage

phi.direct.ct(p, sigmap, X, theta, phi1, phi2, u1, u2, rho)

Arguments

p

vector with the number of 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.

theta

matrix with the estimated log-probabilites of each category in front of the reference category obtained from prmu.time.

phi1

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

phi2

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

u1

matrix with the values of the first random effect obtained from modelfit3.

u2

matrix with the values of the second random effect obtained from modelfit3.

rho

vector with the initial values of the correlation parameter obtained from modelfit3.

Value

a list containing the following components.

phi1.new

vector with the values of the variance component for the first random effect.

phi2.new

vector with the values of the variance component for the second random effect.

rho.new

vector with the correlation parameter.

References

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Small area estimation of labour force indicator 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, Fbetaf.ct sPhikf.ct, ci, modelfit3, msef.ct, mseb, omega

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)

##The variance components
phi.ct=phi.direct.ct(pp,sigmap,datar$X,mean$eta,initial$phi1.0,
       initial$phi2.0,initial$u1.0,initial$u2.0,initial$rho.0)