varmatCUBE {CUB} R Documentation

## 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 `m` Number of ordinal categories `param` Vector of parameters for the specified CUBE 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) `Z` 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. No missing value should be present neither for `ordinal` nor for covariate matrices: thus, deletion or imputation procedures should be preliminarily run.

### 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.

`vcov`, `cormat`

### Examples

```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
naord<-which(is.na(relgoods\$Tv))
nacov<-which(is.na(relgoods\$BirthYear))
na<-union(naord,nacov)
age<-2014-relgoods\$BirthYear[-na]
lage<-log(age)-mean(log(age))
Y<-W<-Z<-lage
ordinal<-relgoods\$Tv[-na]
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)
```

[Package CUB version 1.1.4 Index]