Statistical Methods for Analyzing Ranking Data and their Applications in Business and Social Studies

In many business and social studies involving the comparison of several items, respondents are asked to rank the items according to a certain preference criterion.  In other words, each respondent will provide a ranking of the items, resulting with a dataset of rankings given by the respondents. Recently, Yu (1996) and Yu and Chan (1997) developed two classes of statistical models for analyzing ranking data. They proposed to adopt a Bayesian approach via the Gibbs sampling technique to estimate the model parameters and found that this estimation method is flexible and computationally efficient.  More importantly, their examples showed that both models fit the ranking data well. This project aims (i) to further extend these statistical techniques to handle various complications that may arise in practical situations in business and social studies and (ii) to explore other statistical methods of estimating these new models and to compare their performance with the existing methods.

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Collecting ranking data is fairly common in our daily life but people usually analyze the data wrongly.  Very often, they treat the ranks assigned by the respondents as measured under a continuous scale and then analyze the data using some standard statistical methods such as regression and analysis of variance models.  However, these methods fail to give reliable interpretation of the results because the ordinal structure of the data is not well utilized in these analyses.  Nevertheless, modeling of ranking data is not easy because of various complications.  This project successfully developed suitable ranking models to tackle various complications that may arise in practical situations.  In this project, we have developed relevant statistical models for analyzing ranking data.  These models are rank-ordered probit model, factor model and the model induced by maximum entropy, to explain the individuals’ choice behavior.  To estimate these models, this project successfully developed four estimation approaches, namely a Bayesian approach, MCEM algorithm, simulation-based methods and maximum entropy approach.  As the existing methods for analyzing ranking data in business and social studies lack using the above sophisticated tools, our proposed methods are able to fill this gap and the use of these methods can provide proper and more reliable investigations.

Yu, P.L.H. and Chan K.Y. (2001).   Bayesian analysis of wandering vector models for displaying ranking data.  Statistica Sinica, 2001, Vol.11, 445-461.

 Yu, P.L.H. (2003). Statistical Modelling of ranking data. In Computational Mathematics and Modeling. (Y. Lenbury, N.V. Sanh, Y.H. Wu and B. Wiwatanapataphee Eds.), 319-326.

 Yu, P.L.H. and Chui, S.B.  On simulation-based estimation methods for rank ordered probit models.  Submitted for publication.

 Yu, P.L.H. and Chui, S.B. A maximum entropy approach to recovering information from ranking data. Submitted for publication.

 Yu, P.L.H., Lam, K.F. and Lo, S.M.  Factor analysis for ranking data.  Submitted for publication.

 Two MPhil. Trained.

 Six presentations at international conferences.

Carried extensive simulation studies, parallel programming and data analysis.

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