Pairwise likelihood inference for multivariate categorical responses with application to customer satisfaction

A common practice in customer satisfaction analysis is to administer surveys where subjects are asked to express opinions on a number of statements, or satisfaction scales, by use of ordered categorical responses. Motivated by this application, we propose a pseudo-likelihood approach to estimate the dependence structure among multivariate categorical variables. As it is commonly done in this area, we assume that the responses are related to latent continuous variables which are truncated to induce categorical re- sponses. A Gaussian likelihood is assumed for the latent variables leading to the so called ordered probit model. Since the calculation of the exact likelihood is computationally demanding, we adopt an approximate solution based on pairwise likelihood. To asses the performance of the approach, simulation studies are conducted comparing the proposed method with standard likelihood methods. A parametric bootstrap approach to evaluate the variance of the maximum pairwise likelihood estimator is proposed and discussed. An application to customer satisfaction survey is performed showing the effectiveness of the approach in the presence of covariates and under other generalizations of the model which can make a difference in real data situations