A hierarchical latent variable model for ordinal data from a customer satisfaction survey with “no answer” responses

An item response theory model for ordinal responses proposes that the probability of a particular response from a person on an specific item is a function of latent per- son and question parameters and of cutoffs for the ordinal response categories. This structure was incorporated into a Bayesian hierarchical model by Albert and Chib (1993). We extend their formulation by modeling “No Answer" responses as due to either lack of a strong opinion or indifference to the entire question. In our hierarchical Bayesian framework, prior means for the person and item effects are related to observed covariates. An application of the model to the DuPont Corporation 1992 Engineering Polymers Division Customer Satisfaction Survey is described in detail. The non-conjugate likelihood and prior prevent closed form posterior inference. Three different iterative solutions, using the Griddy Gibbs Sampler (Ritter and Tanner 1992), Metropolis-Hastings Algorithm (Roberts and Smith 1993), and Data Augmentation (Tanner and Wong 1987), are compared. The models are checked using posterior predictive checks (Rubin 1984) and case inuence is diagnosed by importance reweighting (Bradlow and Zaslavsky 1997). The methods illustrated in this research have potential application in other situations in which categorical observations are determined by several latent variables. (March 1999)