A Semiparametric Bayesian Approach for Modelling Ordinal Survey Data with an application to teaching and course evaluations

Abstract

This paper presents a Bayesian latent variable model used to analyze ordinal response survey data by taking into account the characteristics of respondents. The ordinal response data are viewed as multivariate responses arising from continuous latent variables with known cut-points. Each respondent is characterized by two parameters that have a Dirichlet process as their joint prior distribution. The proposed mechanism adjusts for classes of personalities. The model is applied to student survey data in course teaching evaluations. The proposed model is fit and assessed using data obtained from teaching and course evaluations questionnaire containing  m = 15 questions with responses on a five-point scale ranging from 1 (a very negative response) to 5 (a very positive response). Goodness-of-fit (gof) procedures are developed for assessing the validity of the model. The proposed gof procedures are simple, intuitive and do not seem to be a part of current Bayesian practice.  Several simulation studies were also carried out to investigate the model performance. The model identifies areas where performance has been poor or exceptional in a ordinal survey data by investigating standardized parameters. It also allows us to check whether some questions in a survey are redundant.