phi.mult.it: Initial values for the variance components in Model 2
In mme: Multinomial Mixed Effects Models

Description Usage Arguments Value References See Also Examples

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).

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

`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`.

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

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

data.mme, initial.values, wmatrix, prmu.time, Fbetaf.it, phi.direct.it, sPhikf.it, ci, modelfit2, msef.it, mseb.

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)