Main function to estimate and validate a CUSH model for ordinal responses, with or without covariates to explain the shelter effect.
CUSH(Formula,data,...)An object of the class "CUSH" is a list containing the following results:
Maximum likelihood parameters estimates
Log-likelihood function at the final estimates
Variance-covariance matrix of final estimates (if X=0, it returns the square of the estimated standard error for the shelter parameter \(\delta\))
BIC index for the estimated model
Object of class Formula.
Data frame from which model matrices and response variables are taken.
Additional arguments to pass to the fitting procedure. Argument X specifies the matrix of subjects covariates to include in the model for explaining the shelter effect (not including intercept).
The estimation procedure is not iterative, so a null result for CUSH$niter is produced. The optimization procedure is run via "optim". If covariates are included, the variance-covariance matrix is computed as the inverse of the returned numerically differentiated Hessian matrix (option: hessian=TRUE as argument for "optim"). If not positive definite, it returns a warning message and produces a matrix with NA entries.
Capecchi S. and Piccolo D. (2015). Dealing with heterogeneity/uncertainty in sample survey with ordinal data,
IFCS Proceedings, University of Bologna
Capecchi S. and Iannario M. (2016). Gini heterogeneity index for detecting uncertainty in ordinal data surveys,
Metron - DOI: 10.1007/s40300-016-0088-5
loglikCUSH