Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.

Computing marginal likelihoods from a single MCMC output

Abstract: In this article, we propose new Monte Carlo methods for computing a single marginal likelihood or several marginal likelihoods for the purpose of Bayesian model comparisons. The methods are motivated by Bayesian variable selection, in which the marginal likelihoods for all subset variable models are required to compute. The proposed estimates use only a single Markov chain Monte Carlo (MCMC) output from the joint posterior distribution and it does not require the specific structure or the form of the MCMC sampling algorithm that is used to generate the MCMC sample to be known. The theoretical properties of the proposed method are examined in detail. The applicability and usefulness of the proposed method are demonstrated via ordinal data probit regression models. A real dataset involving ordinal outcomes is used to further illustrate the proposed methodology.

Multivariate Analysis and Ordinal Data

Abstract: A test is made of the hypothesis that little error is introduced into multivariate analysis by the assignment of a linear metric to ordinal data. It is shown that previous attempts to test this hypothesis neglected a number of relevant variables. A more thorough test is made which attempts to include all of the relevant variables more or less simultaneously. It is concluded that the error that may result from the arbitrary assignment of equal distance scoring to ordinal variables is greater than has been previously reported. The main reason why the present test of the little error hypothesis reaches a conclusion at variance with previous tests is that they considered only extreme correlations with an outside variable-either perfect or very low.

Interval Censoring and Marginal Analysis in Ordinal Regression

Abstract: This article develops a methodology for regression analysis of ordinal response data subject to interval censoring. This work is motivated by the need to analyze data from multiple studies in toxicological risk assessment. Responses are scored on an ordinal severity scale, but not all responses can be scored completely. For instance, in a mortality study, information on nonfatal but adverse outcomes may be missing. In order to address possible within-study correlations, we develop a generalized estimating approach to the problem, with appropriate adjustments to uncertainty statements. We develop expressions relating parameters of the implied marginal model to the parameters of a conditional model with random effects, and, in a special case, we note an interesting equivalence between conditional and marginal modeling of ordinal responses. We illustrate the methodology in an analysis of a toxicological database.

Fast Bayesian Inference for Non-Conjugate Gaussian Process Regression

Abstract: We present a new variational inference algorithm for Gaussian process regression with non-conjugate likelihood functions, with application to a wide array of problems including binary and multi-class classification, and ordinal regression. Our method constructs a concave lower bound that is optimized using an efficient fixed-point updating algorithm. We show that the new algorithm has highly competitive computational complexity, matching that of alternative approximate inference methods. We also prove that the use of concave variational bounds provides stable and guaranteed convergence - a property not available to other approaches. We show empirically for both binary and multi-class classification that our new algorithm converges much faster than existing variational methods, and without any degradation in performance.

Statistical approaches to analyse patient-reported outcomes as response variables: An application to health-related quality of life:

Abstract: Patient-reported outcomes (PRO) are used as primary endpoints in medical research and their statistical analysis is an important methodological issue. Theoretical assumptions of the selected methodology and interpretation of its results are issues to take into account when selecting an appropriate statistical technique to analyse data. We present eight methods of analysis of a popular PRO tool under different assumptions that lead to different interpretations of the results. All methods were applied to responses obtained from two of the health dimensions of the SF-36 Health Survey. The proposed methods are: multiple linear regression (MLR), with least square and bootstrap estimations, tobit regression, ordinal logistic and probit regressions, beta-binomial regression (BBR), binomial-logit-normal regression (BLNR) and coarsening. Selection of an appropriate model depends not only on its distributional assumptions but also on the continuous or ordinal features of the response and the fact that they are constrained to a bounded interval. The BBR approach renders satisfactory results in a broad number of situations. MLR is not recommended, especially with skewed outcomes. Ordinal methods are only appropriate for outcomes with a few number of categories. Tobit regression is an acceptable option under normality assumptions and in the presence of moderate ceiling or floor effect. The BLNR and coarsening proposals are also acceptable, but only under certain distributional assumptions that are difficult to test a priori. Interpretation of the results is more convenient when using the BBR, BLNR and ordinal logistic regression approaches.