1d:T75f,# Beta-Binomial probabilities of ordinal responses, with feeling and overdispersion parameters for each observation Compute the Beta-Binomial probabilities of ordinal responses, given feeling and overdispersion parameters for each observation. ```r betabinomial(m,ordinal,csivett,phivett) ``` ## Arguments - `m`: Number of ordinal categories - `ordinal`: Vector of ordinal responses. Missing values are not allowed: they should be preliminarily deleted or imputed - `csivett`: Vector of feeling parameters of the Beta-Binomial distribution for given ordinal responses - `phivett`: Vector of overdispersion parameters of the Beta-Binomial distribution for given ordinal responses ## Returns A vector of the same length as ordinal, containing the Beta-Binomial probabilities of each observation, for the corresponding feeling and overdispersion parameters. ## Details The Beta-Binomial distribution is the Binomial distribution in which the probability of success at each trial is random and follows the Beta distribution. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics as an overdispersed binomial distribution. ## Examples ```r data(relgoods) m<-10 ordinal<-relgoods$Tv age<-2014-relgoods$BirthYear no_na<-na.omit(cbind(ordinal,age)) ordinal<-no_na[,1]; age<-no_na[,2] lage<-log(age)-mean(log(age)) gama<-c(-0.6, -0.3) csivett<-logis(lage,gama) alpha<-c(-2.3,0.92); ZZ<-cbind(1,lage) phivett<-exp(ZZ%*%alpha) pr<-betabinomial(m,ordinal,csivett,phivett) plot(density(pr)) ``` ## 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. ## See Also `betar`, `betabinomialcsi`

betabinomial function