CUBE: Main function for CUBE models
In CUB: A Class of Mixture Models for Ordinal Data

Description Usage Arguments Details Value References See Also

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

1	CUBE(Formula,data,...)

`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.

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.

An object of the class "GEM"-"CUBE" is a list containing the following results:

`estimates`	Maximum likelihood estimates: (π, ξ, φ)
`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

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.