varmatCUB {CUB}

Variance-covariance matrix for CUB models

Description

Compute the variance-covariance matrix of parameter estimates for CUB models with or without covariates for the feeling and the uncertainty parameter, and for extended CUB models with shelter effect.

Usage

varmatCUB(ordinal,m,param,Y=0,W=0,X=0,shelter=0)

Arguments

ordinal

Vector of ordinal responses

m

Number of ordinal categories

param

Vector of parameters for the specified CUB model

Y

Matrix of selected covariates to explain the uncertainty component (default: no covariate is included in the model)

W

Matrix of selected covariates to explain the feeling component (default: no covariate is included in the model)

X

Matrix of selected covariates to explain the shelter effect (default: no covariate is included in the model)

shelter

Category corresponding to the shelter choice (default: no shelter effect is included in the model)

Details

The function checks if the variance-covariance matrix is positive-definite: if not, it returns a warning message and produces a matrix with NA entries. No missing value should be present neither for ordinal nor for covariate matrices: thus, deletion or imputation procedures should be preliminarily run.

References

Piccolo D. (2006). Observed Information Matrix for MUB Models, Quaderni di Statistica, 8, 33–78
Iannario, M. (2012). Modelling shelter choices in ordinal data surveys. Statistical Modelling and Applications, 21, 1–22
Iannario M. and Piccolo D. (2016b). A generalized framework for modelling ordinal data. Statistical Methods and Applications, 25, 163–189.

See Also

vcov, cormat

Examples

data(univer)
m<-7
### CUB model with no covariate
pai<-0.87; csi<-0.17 
param<-c(pai,csi)
varmat<-varmatCUB(univer$global,m,param)
#######################
### and with covariates for feeling
data(univer)
m<-7
pai<-0.86; gama<-c(-1.94,-0.17)
param<-c(pai,gama)
ordinal<-univer$willingn; W<-univer$gender      
varmat<-varmatCUB(ordinal,m,param,W)
#######################
### CUB model with uncertainty covariates
data(relgoods)
m<-10
naord<-which(is.na(relgoods$Physician))
nacov<-which(is.na(relgoods$Gender))
na<-union(naord,nacov)
ordinal<-relgoods$Physician[-na]
Y<-relgoods$Gender[-na]
bet<-c(-0.81,0.93); csi<-0.20
varmat<-varmatCUB(ordinal,m,param=c(bet,csi),Y=Y)
#######################
### and with covariates for both parameters
data(relgoods)
m<-10
naord<-which(is.na(relgoods$Physician))
nacov<-which(is.na(relgoods$Gender))
na<-union(naord,nacov)
ordinal<-relgoods$Physician[-na]
W<-Y<-relgoods$Gender[-na]
gama<-c(-0.91,-0.7); bet<-c(-0.81,0.93)
varmat<-varmatCUB(ordinal,m,param=c(bet,gama),Y=Y,W=W)
#######################
### Variance-covariance for a CUB model with shelter
m<-8; n<-300
pai1<-0.5; pai2<-0.3; csi<-0.4
shelter<-6
pr<-probcubshe1(m,pai1,pai2,csi,shelter)
ordinal<-sample(1:m,n,prob=pr,replace=TRUE)
param<-c(pai1,pai2,csi)
varmat<-varmatCUB(ordinal,m,param,shelter=shelter)