9th Biennial ACSPRI Social Science Methodology Conference

Surveys are an important tool in social studies, and most surveys require respondents to rate items on a Likert scale. In this sense, the data collected are often ordinal in nature. This very nature poses challenges to data analysis, as many statistical techniques become inappropriate. In this presentation, a parsimonious mixture distribution, called the combination of uniform and binomial (CUB), which is specifically built for ordinal data, will be revisited. Under CUB, each response is assumed to originate from either the respondent's uncertainty or the actual feeling towards the survey item. In other words, the CUB model can account for respondents' hesitation or indecisiveness towards the survey question, making it a powerful tool to capture the extra variabilities inherent in the responses.

Since most surveys contain more than one question, the data collected are multivariate in nature, and the associations between different survey items are usually of considerable interest. An extension of the univariate CUB model to the bivariate case will be introduced. Most of the previous attempts employed the method of copula, which makes interpretation difficult. In the opposite, our proposed method bypasses the use of copula and allows the associations between the unobserved uncertainty and feeling components of the responses to be estimated. This distinctive feature makes our proposed model more interpretable compared to copula-based ones. In addition, the model parameters can be shown to be identifiable, making the model statistically valid.

Such a bivariate CUB model can serve as a tool for analysing survey data in social sciences and other disciplines. This presentation will describe the underlying logic and both theoretical and practical aspects of the proposed model, and will demonstrate its application through a real-word example.