Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2755

Full Length Research Paper

A Bayesian analysis of bivariate ordered categorical responses using a latent variable regression model: Application to diabetic retinopathy data

  Anoshirvan Kazemnejad1, Farid Zayeri2, Nor Aishah Hamzah3, Rasool Gharaaghaji4, Masoud Salehi5
1Department of Biostatistics, School of Medical Sciences, Tarbiat Modares University, P.O. Box: 14115-111, Tehran, Iran. 2Department of Biostatistics, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran. 3Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia. 4Department of Biostatistics and Epidemiology, Faculty of Medicine, Urmia University of Medical Sciences, Urmia, Iran. 5Department of Statistics and Mathematics, Faculty of Management and Medical Informatics, Iran University of Medical Sciences, Tehran, Iran.
Email: Anoshirvan Kazemnejad1, Farid Zayeri2, Nor Aishah Hamzah3, Rasool Gharaaghaji4, Masoud Salehi5

  •  Accepted: 25 March 2010
  •  Published: 04 June 2010


Latent variable distribution models are frequently utilized for analyzing bivariate ordered categorical response data. In this context, choosing the bivariate normal distribution as the underlying latent distribution, which leads to the bivariate cumulative probit model, is the most common strategy for analyzing theses data sets. However, when the conditional distribution of the available bivariate response has an asymmetric form, other convenient asymmetric bivariate distributions may lead to a better fit. In this paper, we use an asymmetric bivariate cumulative latent variable distribution model for analyzing bivariate ordered categorical response data. For estimating the model parameters, we use two strategies: maximum likelihood and Bayesian approaches. We also use the proposed model for analyzing the data from 623 diabetic patients to identify some of the most important risk indicators of diabetic retinopathy among them. The obtained results revealed that patients’ age at diagnosis, duration of diabetes, HbA1c, method of diabetes control, macular edema, and presence of hypertension and renal disease are significantly associated with the severity of diabetic retinopathy. In conclusion, both the maximum likelihood and Bayesian analyses resulted in similar significant risk indicators. However, it seems that the Bayesian analysis gives us smaller standard errors compared to the maximum likelihood approach.


Key words: Latent variable, bivariate ordinal response, asymmetric distribution, maximum likelihood estimation, Bayesian estimation, diabetic retinopathy.