publication . Preprint . Article . Other literature type . 2015

Bayesian Model Choice in Cumulative Link Ordinal Regression Models

McKinley, Trevelyan J.; Morters, Michelle; Wood, James L. N.;
Open Access English
  • Published: 28 Jan 2015
  • Country: United Kingdom
Abstract
The use of the proportional odds (PO) model for ordinal regression is ubiquitous in the literature. If the assumption of parallel lines does not hold for the data, then an alternative is to specify a non-proportional odds (NPO) model, where the regression parameters are allowed to vary depending on the level of the response. However, it is often difficult to fit these models, and challenges regarding model choice and fitting are further compounded if there are a large number of explanatory variables. We make two contributions towards tackling these issues: firstly, we develop a Bayesian method for fitting these models, that ensures the stochastic ordering condit...
Subjects
free text keywords: Bayesian inference, ordinal regression, Markov chain Monte Carlo, reversible-jump, Bayesian model choice, Statistics - Methodology, Mathematics - Statistics Theory
Related Organizations
61 references, page 1 of 5

Agresti, A. (2010). Analysis of Ordinal Categorical Data. Wiley, 2nd edition. 2, 7, 8

Akaike, H. (1974). “A new look at statistical model identification.” IEEE Transactions on Automatic Control , AU-19: 195-223. 3

Albert, J. and Chib, S. (1997). “Bayesian methods for cumulative, sequential and twostep ordinal data regression models.” Technical report. 4, 8

Albert, J. H. and Chib, S. (1993). “Bayesian analysis of binary and polychotomous response data.” Journal of the American Statistical Association, 88(422): 669-679. 1, 3, 7 [OpenAIRE]

Ananth, C. V. and Kleinbaum, D. G. (1997). “Regression models for ordinal responses: A review of methods and applications.” International Journal of Epidemiology, 26(6): 1323-1333. 2 [OpenAIRE]

Bender, R. and Grouven, U. (1998). “Using binary logistic regression models for ordinal data with non-proportional odds.” Journal of Clinical Epidemiology, 51(10): 809-816. 2, 8, 16

Brant, R. (1990). “Assessing proportionality in the proportional odds model for ordinal logistic regression.” Biometrics, 46(4): 1171-1178. 2 [OpenAIRE]

Brooks, S. P., Giudici, P., and Roberts, G. O. (2003). “Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions.” Journal of the Royal Statistical Society. Series B (Methodological), 65(1): 3-55. 13

Chib, S. (1995). “Marginal likelihood from the Gibbs output.” Journal of the American Statistical Association, 90(432): 1313-1321. 4 [OpenAIRE]

Chu, W. and Ghahramani, Z. (2005). “Gaussian processes for ordinal regression.” Journal of Machine Learning Research, 6: 1-48. 3, 4

Cole, S. R., Allison, P. D., and Ananth, C. V. (2004). “Estimation of cumulative odds ratios.” Annals of Epidemiology, 14: 172-178. 2

Congdon, P. (2005). Bayesian Models for Categorical Data. Wiley. 7, 8

Dellaportas, P., Forster, J. J., and Ntzoufras, I. (2002). “On Bayesian model and variable selection using MCMC.” Statistics and Computing, 12: 27-36. 4, 6

Diggle, P. J., Heagerty, P., Liang, K.-Y., and Zeger, S. L. (2002). Analysis of Longitudinal Data. Oxford University Press, 2nd edition. 3

Fahrmeier, L. and Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer. 8

61 references, page 1 of 5
Abstract
The use of the proportional odds (PO) model for ordinal regression is ubiquitous in the literature. If the assumption of parallel lines does not hold for the data, then an alternative is to specify a non-proportional odds (NPO) model, where the regression parameters are allowed to vary depending on the level of the response. However, it is often difficult to fit these models, and challenges regarding model choice and fitting are further compounded if there are a large number of explanatory variables. We make two contributions towards tackling these issues: firstly, we develop a Bayesian method for fitting these models, that ensures the stochastic ordering condit...
Subjects
free text keywords: Bayesian inference, ordinal regression, Markov chain Monte Carlo, reversible-jump, Bayesian model choice, Statistics - Methodology, Mathematics - Statistics Theory
Related Organizations
61 references, page 1 of 5

Agresti, A. (2010). Analysis of Ordinal Categorical Data. Wiley, 2nd edition. 2, 7, 8

Akaike, H. (1974). “A new look at statistical model identification.” IEEE Transactions on Automatic Control , AU-19: 195-223. 3

Albert, J. and Chib, S. (1997). “Bayesian methods for cumulative, sequential and twostep ordinal data regression models.” Technical report. 4, 8

Albert, J. H. and Chib, S. (1993). “Bayesian analysis of binary and polychotomous response data.” Journal of the American Statistical Association, 88(422): 669-679. 1, 3, 7 [OpenAIRE]

Ananth, C. V. and Kleinbaum, D. G. (1997). “Regression models for ordinal responses: A review of methods and applications.” International Journal of Epidemiology, 26(6): 1323-1333. 2 [OpenAIRE]

Bender, R. and Grouven, U. (1998). “Using binary logistic regression models for ordinal data with non-proportional odds.” Journal of Clinical Epidemiology, 51(10): 809-816. 2, 8, 16

Brant, R. (1990). “Assessing proportionality in the proportional odds model for ordinal logistic regression.” Biometrics, 46(4): 1171-1178. 2 [OpenAIRE]

Brooks, S. P., Giudici, P., and Roberts, G. O. (2003). “Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions.” Journal of the Royal Statistical Society. Series B (Methodological), 65(1): 3-55. 13

Chib, S. (1995). “Marginal likelihood from the Gibbs output.” Journal of the American Statistical Association, 90(432): 1313-1321. 4 [OpenAIRE]

Chu, W. and Ghahramani, Z. (2005). “Gaussian processes for ordinal regression.” Journal of Machine Learning Research, 6: 1-48. 3, 4

Cole, S. R., Allison, P. D., and Ananth, C. V. (2004). “Estimation of cumulative odds ratios.” Annals of Epidemiology, 14: 172-178. 2

Congdon, P. (2005). Bayesian Models for Categorical Data. Wiley. 7, 8

Dellaportas, P., Forster, J. J., and Ntzoufras, I. (2002). “On Bayesian model and variable selection using MCMC.” Statistics and Computing, 12: 27-36. 4, 6

Diggle, P. J., Heagerty, P., Liang, K.-Y., and Zeger, S. L. (2002). Analysis of Longitudinal Data. Oxford University Press, 2nd edition. 3

Fahrmeier, L. and Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer. 8

61 references, page 1 of 5
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