Topic
Ordinal regression
About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.
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01 Jan 2006
TL;DR: Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas.
Abstract: Regression models are frequently used to develop diagnostic, prognostic, and health resource utilization models in clinical, health services, outcomes, pharmacoeconomic, and epidemiologic research, and in a multitude of non-health-related areas. Regression models are also used to adjust for patient heterogeneity in randomized clinical trials, to obtain tests that are more powerful and valid than unadjusted treatment comparisons.
4,211 citations
TL;DR: In this article, a general class of regression models for ordinal data is developed and discussed, which utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality.
Abstract: SUMMARY A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.
3,647 citations
TL;DR: In this article, an extension of the dichotomous probit model for ordinal dependent variables is presented. But the model assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an interval level variable.
Abstract: This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.
2,520 citations
TL;DR: Gologit2 as discussed by the authors is a generalized ordered logit model inspired by Vincent Fu's gologit routine (Stata Technical Bulletin Reprints 8: 160-164).
Abstract: This article describes the gologit2 program for generalized ordered logit models. gologit2 is inspired by Vincent Fu's gologit routine (Stata Technical Bulletin Reprints 8: 160–164) and is backward...
1,805 citations
Book•
01 Jan 1984
TL;DR: In this article, the authors present a survey of the advantages of using logit models in regression models for Ordinal Probabilities, Scores, and Odds Ratios, as well as their drawbacks.
Abstract: Preface. 1. Introduction. 1.1. Ordinal Categorical Scales. 1.2. Advantages of Using Ordinal Methods. 1.3. Ordinal Modeling Versus Ordinary Regession Analysis. 1.4. Organization of This Book. 2. Ordinal Probabilities, Scores, and Odds Ratios. 2.1. Probabilities and Scores for an Ordered Categorical Scale. 2.2. Ordinal Odds Ratios for Contingency Tables. 2.3. Confidence Intervals for Ordinal Association Measures. 2.4. Conditional Association in Three-Way Tables. 2.5. Category Choice for Ordinal Variables. Chapter Notes. Exercises. 3. Logistic Regression Models Using Cumulative Logits. 3.1. Types of Logits for An Ordinal Response. 3.2. Cumulative Logit Models. 3.3. Proportional Odds Models: Properties and Interpretations. 3.4. Fitting and Inference for Cumulative Logit Models. 3.5. Checking Cumulative Logit Models. 3.6. Cumulative Logit Models Without Proportional Odds. 3.7. Connections with Nonparametric Rank Methods. Chapter Notes. Exercises. 4. Other Ordinal Logistic Regression Models. 4.1. Adjacent-Categories Logit Models. 4.2. Continuation-Ratio Logit Models. 4.3. Stereotype Model: Multiplicative Paired-Category Logits. Chapter Notes. Exercises. 5. Other Ordinal Multinomial Response Models. 5.1. Cumulative Link Models. 5.2. Cumulative Probit Models. 5.3. Cumulative Log-Log Links: Proportional Hazards Modeling. 5.4. Modeling Location and Dispersion Effects. 5.5. Ordinal ROC Curve Estimation. 5.6. Mean Response Models. Chapter Notes. Exercises. 6. Modeling Ordinal Association Structure. 6.1. Ordinary Loglinear Modeling. 6.2. Loglinear Model of Linear-by-Linear Association. 6.3. Row or Column Effects Association Models. 6.4. Association Models for Multiway Tables. 6.5. Multiplicative Association and Correlation Models. 6.6. Modeling Global Odds Ratios and Other Associations. Chapter Notes. Exercises. 7. Non-Model-Based Analysis of Ordinal Association. 7.1. Concordance and Discordance Measures of Association. 7.2. Correlation Measures for Contingency Tables. 7.3. Non-Model-Based Inference for Ordinal Association Measures. 7.4. Comparing Singly Ordered Multinomials. 7.5. Order-Restricted Inference with Inequality Constraints. 7.6. Small-Sample Ordinal Tests of Independence. 7.7. Other Rank-Based Statistical Methods for Ordered Categories. Appendix: Standard Errors for Ordinal Measures. Chapter Notes. Exercises. 8. Matched-Pairs Data with Ordered Categories. 8.1. Comparing Marginal Distributions for Matched Pairs. 8.2. Models Comparing Matched Marginal Distributions. 8.3. Models for The Joint Distribution in A Square Table. 8.4. Comparing Marginal Distributions for Matched Sets. 8.5. Analyzing Rater Agreement on an Ordinal Scale. 8.6. Modeling Ordinal Paired Preferences. Chapter Notes. Exercises. 9. Clustered Ordinal Responses: Marginal Models. 9.1. Marginal Ordinal Modeling with Explanatory Variables. 9.2. Marginal Ordinal Modeling: GEE Methods. 9.3. Transitional Ordinal Modeling, Given the Past. Chapter Notes. Exercises. 10. Clustered Ordinal Responses: Random Effects Models. 10.1. Ordinal Generalized Linear Mixed Models. 10.2. Examples of Ordinal Random Intercept Models. 10.3. Models with Multiple Random Effects. 10.4. Multilevel (Hierarchical) Ordinal Models. 10.5. Comparing Random Effects Models and Marginal Models. Chapter Notes. Exercises. 11. Bayesian Inference for Ordinal Response Data. 11.1. Bayesian Approach to Statistical Inference. 11.2. Estimating Multinomial Parameters. 11.3. Bayesian Ordinal Regression Modeling. 11.4. Bayesian Ordinal Association Modeling. 11.5. Bayesian Ordinal Multivariate Regression Modeling. 11.6. Bayesian Versus Frequentist Approaches to Analyzing Ordinal Data. Chapter Notes. Exercises. Appendix Software for Analyzing Ordinal Categorical Data. Bibliography. Example Index. Subject Index.
1,678 citations