omega: Model correlation matrix for Model 3
In mme: Multinomial Mixed Effects Models

Description Usage Arguments Value References See Also Examples

This function calculates the model correlation matrix and the first derivative of the model correlation matrix for Model 3. Model 3 is 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.

1	omega(t, k, rho, phi2)

`t`	number of time periods.
`k`	number of categories of the response variable.
`rho`	vector with the correlation parameter obtained from `modelfit3`.
`phi2`	vector with the values of the second variance component obtained from `modelfit3`.

A list containing the following components.

`Omega.d`	correlation matrix.
`First.derivative.Omegad`	Fisher derivative of the model correlation matrix.

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.

data.mme, initial.values, wmatrix ,phi.mult.ct, prmu.time, phi.direct.ct, Fbetaf.ct, sPhikf.ct, ci, modelfit3, msef.ct, mseb

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)

##The model correlation matrix
matrix.corr=omega(datar$t,k,initial$rho.0,initial$phi2.0)