modelfit2 {mme}

Function to fit Model 2

Description

This function fits the multinomial mixed model with two independent random effects for each category of the response variable: one domain random effect and another independent time and domain random effect (Model 2). The formulation is described in Lopez-Vizcaino et al. (2013). The fitting algorithm combines the penalized quasi-likelihood method (PQL) for estimating and predicting the fixed and random effects, respectively, with the residual maximum likelihood method (REML) for estimating the variance components. This function uses as initial values the output of the function initial.values.

Usage

modelfit2(d, t, pp, Xk, X, Z, initial, y, M, MM)

Arguments

d

number of areas.

t

number of time periods.

pp

vector with the number of the auxiliary variables per category.

Xk

list of matrices with the auxiliary variables per category obtained from data.mme. The dimension of the list is the number of domains.

X

list of matrices with the auxiliary variables obtained from data.mme. The dimension of the list is the number of categories of the response variable minus one.

Z

design matrix of random effects data.mme.

initial

output of the function initial.values.

y

matrix with the response variable obtained from data.mme, except the reference category. The rows are the domains and the columns are the categories of the response variable minus one.

M

vector with the area sample sizes.

MM

vector with the population sample sizes.

Value

A list containing the following components.

Estimated.probabilities

matrix with the estimated probabilities for the categories of response variable.

Fisher.information.matrix.phi

Fisher information matrix of the variance components.

Fisher.information.matrix.beta

Fisher information matrix of the fixed effects.

u1

matrix with the estimated first random effect.

u2

matrix with the estimated second random effect.

mean

matrix with the estimated mean of response variable.

warning1

0=OK,1=The model could not be fitted.

warning2

0=OK,1=The value of the variance component is negative: the initial value is taken.

beta.Stddev.p.value

matrix with the estimated fixed effects, its standard deviations and its p-values.

phi.Stddev.p.value

matrix with the estimated variance components, its standard deviations and its p-values.

References

Lopez-Vizcaino, ME, Lombardia, MJ and Morales, D (2013). Small area estimation of labour force indicators under a multinomial mixed model with correlated time and area effects. Submitted for review.

See Also

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

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=2 #type of model
data(simdata2)  #data
datar=data.mme(simdata2,k,pp,mod)

##Model fit
result=modelfit2(datar$d,datar$t,pp,datar$Xk,datar$X,datar$Z,datar$initial,datar$y[,1:(k-1)],
       datar$n,datar$N)