IHG: Main function for IHG models

Description

Main function to estimate and validate an Inverse Hypergeometric model, without or with covariates for explaining the preference parameter.

Usage

IHG(Formula, data, ...)

Value

An object of the class "IHG" 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 no covariate is included in the model, it returns the square of the estimated standard error for the preference parameter $\theta$
BIC: BIC index for the estimated model

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 U specifies the matrix of subjects covariates to include in the model for explaining the preference parameter (not including intercept).

Details

This is the main function for IHG models (that are nested into CUBE models, see the references below), calling for the corresponding function whenever covariates are specified.
The parameter $\theta$ represents the probability of observing a rating corresponding to the first category and is therefore a direct measure of preference, attraction, pleasantness toward the investigated item. This is reason why $\theta$ is customarily referred to as the preference parameter of the IHG model.
The estimation procedure is not iterative, so a null result for IHG$niter is produced.
The optimization procedure is run via "optim". The variance-covariance matrix (or the estimated standard error for theta if no covariate is included) 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