varmatCUB function

Variance-covariance matrix for CUB models

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.

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.

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)

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