varmatCUB {CUB} | R Documentation |
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
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)