omega function

Model correlation matrix for Model 3

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.

omega(t, k, rho, phi2)

Arguments

• 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.

Returns

A list containing the following components. - Omega.d: correlation matrix.

• First.derivative.Omegad: Fisher derivative of the model correlation matrix.

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)

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

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.

See Also

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