CUBE function

Main function for CUBE models

Main function to estimate and validate a CUBE model for given ratings, explaining uncertainty, feeling and overdispersion.

CUBE(Formula,data,...)

Arguments

• Formula: Object of class Formula.
• data: Data frame from which model matrices and response variables are taken.
• ...: Additional arguments to be passed for the specification of the model, Including Y, W, Z for explanatory variables for uncertainty, feeling and overdispersion. Set expinform=TRUE if inference should be based on expected information matrix for model with no covariate. Set starting = ... to pass initial values for EM iterations.

Returns

An object of the class "GEM"-"CUBE" is a list containing the following results: - estimates: Maximum likelihood estimates: $(\pi, \xi, \phi)$

• loglik: Log-likelihood function at the final estimates

• varmat: Variance-covariance matrix of final estimates

• niter: Number of executed iterations

• BIC: BIC index for the estimated model

Details

It is the main function for CUBE models, calling for the corresponding functions whenever covariates are specified: it is possible to select covariates for explaining all the three parameters or only the feeling component.

The program also checks if the estimated variance-covariance matrix is positive definite: if not, it prints a warning message and returns a matrix and related results with NA entries. The optimization procedure is run via "optim". If covariates are included only for feeling, the variance-covariance matrix is computed as the inverse of the returned numerically differentiated Hessian matrix (option: hessian=TRUE as argument for "optim"), and the estimation procedure is not iterative, so a NULL result for $niter is produced. If the estimated variance-covariance matrix is not positive definite, the function 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.

Iannario M. (2015). Detecting latent components in ordinal data with overdispersion by means of a mixture distribution, Quality & Quantity, 49 , 977--987

Iannario M. (2016). Testing the overdispersion parameter in CUBE models. Communications in Statistics: Simulation and Computation, 45 (5), 1621--1635.

See Also

probcube, loglikCUBE, loglikcuben, inibestcube, inibestcubecsi, inibestcubecov, varmatCUBE