varmatCUBE: Variance-covariance matrix for CUBE models

Description

Compute the variance-covariance matrix of parameter estimates for CUBE models when no covariate is specified, or when covariates are included for all the three parameters.

Usage

varmatCUBE(ordinal,m,param,Y=0,W=0,Z=0,expinform=FALSE)

Arguments

ordinal

Vector of ordinal responses

Number of ordinal categories

param

Vector of parameters for the specified CUBE model

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

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

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

expinform

Logical: if TRUE and no covariate is included in the model, the function returns the expected variance-covariance matrix (default is FALSE: the function returns the observed variance-covariance matrix)

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.

References

Iannario, M. (2014). Modelling Uncertainty and Overdispersion in Ordinal Data, Communications in Statistics - Theory and Methods, 43, 771--786 Piccolo D. (2015). Inferential issues for CUBE models with covariates, Communications in Statistics. Theory and Methods, 44(23), 771--786.

Examples

Run this code

m<-7; n<-500
pai<-0.83; csi<-0.19; phi<-0.045
ordinal<-simcube(n,m,pai,csi,phi)
param<-c(pai,csi,phi)
varmat<-varmatCUBE(ordinal,m,param)
##########################
### Including covariates

data(relgoods)
m<-10
ordinal<-relgoods[,37]
age<-2014-relgoods[,4]
lage<-log(age)-mean(log(age))
nona<-na.omit(cbind(ordinal,lage))
ordinal<-nona[,1]
Y<-W<-Z<-nona[,2]
estbet<-c(0.18, 1.03); estgama<-c(-0.6, -0.3); estalpha<-c(-2.3,0.92)
param<-c(estbet,estgama,estalpha)
varmat<-varmatCUBE(ordinal, m, param, Y=Y, W=W, Z=Z, expinform=TRUE)