prmu.time: Estimated mean and probabilities for Model 2 and 3
In mme: Multinomial Mixed Effects Models

Description Usage Arguments Value References See Also Examples

This function calculates the estimated probabilities and the estimated mean of the response variable, in the multinomial mixed models with two independent random effects, one random effect associated with the area and the other associated with the time, for each category of the response variable. The first model assumes independent time and domain random effect (Model 2) and the second model assumes correlated time and domain random effect (Model 3).

1	prmu.time(M, Xk, beta, u1, u2)

`M`	vector with the area sample sizes.
`Xk`	list of matrices with the auxiliary variables per category obtained from `data.mme`. The dimension of the list is the number of domains.
`beta`	a list with the values for the fixed effects beta per category obtained from `modelfit2`.
`u1`	a vector with the values of the first random effect obtained from `modelfit2` or `modelfit3`.
`u2`	a vector with the values of the second random effect obtained from `modelfit2` or `modelfit3`.

A list containing the following components:

`Estimated.probabilities`	matrix with the estimated probabilities for the categories of response variable.
`mean`	matrix with the estimated mean of the response variable.
`eta`	matrix with the estimated log-rates of the probabilities of each category over the reference category.

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. Submited for review.

data.mme, initial.values, wmatrix, phi.mult.it, 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
mod=2 #Type of model
data(simdata2) # data
datar=data.mme(simdata2,k,pp,mod)
initial=datar$initial

## Estimated mean and estimated probabilities
mean=prmu.time(datar$n,datar$Xk,initial$beta.0,initial$u1.0,initial$u2.0)