prmu: Estimated mean and probabilities for Model 1 In mme: Multinomial Mixed Effects Models

Description

This function calculates the estimated probabilities and the estimated mean of the response variable, in the multinomial mixed model with one independent random effect in each category of the response variable (Model 1).

Usage

 `1` ```prmu(M, Xk, beta, u) ```

Arguments

 `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` fixed effects obtained from `modelfit1`. `u` values of random effects obtained from `modelfit1`.

Value

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.

References

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`, `phi.mult`, `Fbetaf`, `phi.direct`, `sPhikf`, `ci`, `modelfit1`, `msef`, `mseb`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```k=3 #number of categories of the response variable pp=c(1,1) #vector with the number of auxiliary variables in each category data(simdata) #data mod=1 #type of model D=nrow(simdata) datar=data.mme(simdata,k,pp,mod) initial=datar\$initial ##Estimated mean and probabilities mean=prmu(datar\$n,datar\$Xk,initial\$beta.0,initial\$u.0) ```