CUB (version 0.1)

CUB: Main function for CUB models

Description

Main function to estimate and validate a CUB model for explaining uncertainty and feeling for given ratings, with or without covariates and shelter effect.

Usage

CUB(ordinal,m=get('m',envir=.GlobalEnv),
Y=0,W=0,shelter=0,maxiter,toler,makeplot=TRUE,summary=TRUE)

Arguments

ordinal

Vector of ordinal responses

m

Number of ordinal categories (if omitted, it will be assigned to the number of categories specified in the global environment)

Y

Matrix of covariates for explaining the uncertainty component. If omitted (default), no covariate is included in the model

W

Matrix of covariates for explaining the feeling component. If omitted (default), no covariate is included in the model

shelter

Category corresponding to the shelter choice. If omitted (default), no shelter effect is included in the model

maxiter

Maximum number of iterations allowed for running the optimization algorithm (default: maxiter=500)

toler

Fixed error tolerance for final estimates (default: toler = 1e-4)

makeplot

Logical: if TRUE (default), the algorithm returns a graphical plot comparing fitted probabilities and observed relative frequencies for CUB models without covariates. If only one explicative dichotomous variable is included in the model for the feeling or the uncertainty components, then the function returns a graphical plot comparing the distributions of the responses conditioned to the value of the covariate

summary

Logical: if TRUE (default), summary results of the fitting procedure are displayed on screen

Value

An object of the class "CUB" is a list containing the following results:

estimates

Maximum likelihood estimates: $(\pi, \xi)$

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

This is the main function for CUB models, which calls for the corresponding functions whenever covariates or shelter effect are specified. It performs maximum likelihood estimation via the E-M algorithm for CUB models and extensions. The optimization procedure is run via "optim". It is possible to fit data with CUB models, with or without covariates for the parameters of the mixture model, and CUB models with shelter effect with no covariate included in the model. 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.

References

Piccolo D. and D'Elia A. (2008). A new approach for modelling consumers' preferences, Food Quality and Preference, 18, 247--259 Iannario M. and Piccolo D. (2012). CUB models: Statistical methods and empirical evidence, in: Kenett R. S. and Salini S. (eds.), Modern Analysis of Customer Surveys: with applications using R, J. Wiley and Sons, Chichester, 231--258 Iannario M. (2012). Modelling shelter choices in a class of mixture models for ordinal responses, Statistical Methods and Applications, 21, 1--22 Iannario M. and Piccolo D. (2014). Inference for CUB models: a program in R, Statistica & Applicazioni, XII n.2, 177--204 Iannario M. (2016). Testing the overdispersion parameter in CUBE models, Communications in Statistics: Simulation and Computation, 45(5), 1621--1635

See Also

probcub00, probcubp0, probcub0q, probcubpq, probcubshe1, loglikCUB, varmatCUB

Examples

data(relgoods)
m<-10
ordinal<-na.omit(relgoods[,40]) 
model<-CUB(ordinal)      # Equivalent calls: CUB(ordinal, m) or CUB(ordinal,m=10) 
                         # if m has not been previously declared
estpar<-model$estimates  # Estimated parameter vector (pai,csi)
maxlik<-model$loglik     # Log-likelihood function at ML estimates
vmat<-model$varmat
nniter<-model$niter
BICCUB<-model$BIC
################
## CUB model
data(univer)
m<-7
officeho<-univer[,10]
model<-CUB(officeho,shelter=7)
BICcub<-model$BIC
################
## CUB model with covariate for uncertainty
data(relgoods)
m<-10
ordinal<-relgoods[,26] 
gender<-relgoods[,7]
data<-na.omit(cbind(ordinal,gender))
modelcovpai<-CUB(data[,1],Y=data[,2])
BICcovpai<-modelcovpai$BIC
## CUB model with covariate for feeling
data(univer)
m<-7
ordinal<-univer[,12]
freqserv<-univer[,2]
modelcovcsi<-CUB(ordinal,W=freqserv)
##################
## CUB model with covariates for both components
data(univer)
m<-7
gender<-univer[,4]
lage<-log(univer[,3])-mean(log(univer[,3]))
ordinal<-univer[,12]
maxiter<-500; toler<-1e-6;
model<-CUB(ordinal,Y=gender,W=lage) # Makeplot is ignored
param<-model$estimates
bet<-param[1:2]      # ML estimates of coefficients for uncertainty covariate
gama<-param[3:4]     # ML estimates of coefficients for feeling covariate