phi.mult.it {mme}

Initial values for the variance components in Model 2

Description

This function is used in initial.values to calculate the initial values for the variance components in the multinomial mixed model with two independent random effects for each category of the response variable: one domain random effect (u1) and another independent time and domain random effect (u2) (Model 2).

Usage

phi.mult.it(beta.0, y, Xk, M, u1, u2)

Arguments

beta.0

initial values for the fixed effects obtained from initial.values.

y

matrix with the response variable obtained from data.mme. The rows are the domains and the columns are the categories of the response variable.

Xk

list of matrices with the auxiliary variables per category obtained from data.mme. The dimension of the list is the number of domains.

M

vector with the sample size of the areas.

u1

vector with the initial values for the first random effect obtained from initial.values.

u2

vector with the initial values for the second random effect obtained from initial.values.

Value

phi.0 vector of the initial values for the variance components.

References

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

See Also

data.mme, initial.values, wmatrix, prmu.time, Fbetaf.it, phi.direct.it, sPhikf.it, ci, modelfit2, msef.it, 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(simdata2)  #data
mod=2 #Type of model
datar=data.mme(simdata2,k,pp,mod)
D=nrow(simdata2)
###fixed effects values
beta.new=list()
beta.new[[1]]=matrix(c( 1.3,-1),2,1)
beta.new[[2]]=matrix(c( -1.6,1),2,1)
## random effects values
u1.new=rep(0.01,((k-1)*datar$d))
dim(u1.new)=c(datar$d,k-1)
u2.new=rep(0.01,((k-1)*D))
dim(u2.new)=c(D,k-1)

##Initial variance components
phi=phi.mult.it(beta.new,datar$y,datar$Xk,datar$n,u1.new,u2.new)