CUB (version 0.1)

probcubshe3: probcubshe3

Description

Probability distribution of a CUB model with explicit shelter effect: satisficing interpretation

Usage

probcubshe3(m, lambda, eta, csi, shelter)

Arguments

m

Number of ordinal categories

lambda

Mixing coefficient for the shifted Binomial component

eta

Mixing coefficient for the mixture of the uncertainty component and the shelter effect

csi

Feeling parameter

shelter

Category corresponding to the shelter choice

Value

The vector of the probability distribution of a CUB model with shelter effect

Details

The "satisficing interpretation" provides a parametrization for CUB models with explicit shelter effect as a mixture of two components: a shifted Binomial distribution with feeling parameter $\xi$ (meditated choice), and a mixture of a degenerate distribution with unit mass at the shelter category ("shelter") and a discrete uniform distribution over $m$ categories, with mixing coefficient specified by $\eta$ (lazy selection of a category). Both components of the mixtures are weighted by $\lambda$ coefficient.

References

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. and Piccolo D. (2014). A comprehensive approach to ordinal data modelling, Working paper

See Also

probcubshe1, probcubshe2

Examples

m<-8
pai1<-0.5
pai2<-0.3
csi<-0.4
shelter<-6
lambda<-pai1
eta<-1-pai2/(1-pai1)
pr3<-probcubshe3(m, lambda, eta, csi, shelter)
plot(1:m,pr3,type="h", main="CUB probability distribution with explicit 
shelter effect",xlab="Ordinal categories")
points(1:m,pr3,pch=19)