CUSH function

Main function for CUSH models

Main function to estimate and validate a CUSH model for ordinal responses, with or without covariates to explain the shelter effect.

CUSH(Formula,data,...)

Arguments

• Formula: Object of class Formula.
• data: 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).

Returns

An object of the class "CUSH" is a list containing the following results: - estimates: Maximum likelihood parameters estimates

• loglik: Log-likelihood function at the final estimates

• varmat: Variance-covariance matrix of final estimates (if X=0, it returns the square of the estimated standard error for the shelter parameter $\delta$)

• BIC: BIC index for the estimated model

Details

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.

References

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

See Also

loglikCUSH