Ordinal regression

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

Marginal Regression Models for Clustered Ordinal Measurements

Abstract: This article constructs statistical models for clustered ordinal measurements. We specify two regression models: one for the marginal means and one for the marginal pairwise global odds ratios. Of particular interest are problems in which the odds ratio regression is a focus. Simple assumptions about higher-order conditional moments give a quadratic exponential likelihood function with second-order estimating equations (GEE2) as score equations. But computational difficulty can arise for large clusters when both the mean response and the association between measures is of interest. First, we present GEE1 as an alternative estimation strategy. Second, we extend to repeated ordinal measurements the method developed by Carey et al. for binary observations that is based on alternating logistic regressions (ALR) for the marginal mean parameters and the pairwise log-odds ratio parameters. We study the efficiency of GEE1 and ALR relative to full maximum likelihood. We demonstrate the utility of our regr...

Fitting heterogeneous choice models with oglm

Abstract: When a binary or ordinal regression model incorrectly assumes that er- ror variances are the same for all cases, the standard errors are wrong and (unlike ordinary least squares regression) the parameter estimates are biased Hetero- geneous choice models (also known as location-scale models or heteroskedastic ordered models) explicitly specify the determinants of heteroskedasticity in an at- tempt to correct for it Such models are also useful when the variance itself is of substantive interest This article illustrates how the author's Stata program oglm (ordinal generalized linear models) can be used to fit heterogeneous choice and related models It shows that two other models that have appeared in the liter- ature (Allison's model for group comparisons and Hauser and Andrew's logistic response model with proportionality constraints) are special cases of a heteroge- neous choice model and alternative parameterizations of it The article further argues that heterogeneous choice models may sometimes be an attractive alterna- tive to other ordinal regression models, such as the generalized ordered logit model fit by gologit2 Finally, the article offers guidelines on how to interpret, test, and modify heterogeneous choice models

Ordinal response regression models in ecology.

Abstract: . Although ordinal data are not rare in ecology, ecological studies have, until now, seriously neglected the use of specific ordinal regression models. Here, we present three models – the Proportional Odds, the Continuation Ratio and the Stereotype models – that can be successfully applied to ordinal data. Their differences and respective fields of application are discussed. Finally, as an example of application, PO models are used to predict spatial abundance of plant species in a Geographical Information System. It shows that ordinal models give as good a result as binary logistic models for predicting presence-absence, but are additionally able to predict abundance satisfactorily.

Distinguishing ordinal and disordinal interactions.

Abstract: Re-parameterized regression models may enable tests of crucial theoretical predictions involving interactive effects of predictors that cannot be tested directly using standard approaches. First, we present a re-parameterized regression model for the Linear × Linear interaction of 2 quantitative predictors that yields point and interval estimates of 1 key parameter-the crossover point of predicted values-and leaves certain other parameters unchanged. We explain how resulting parameter estimates provide direct evidence for distinguishing ordinal from disordinal interactions. We generalize the re-parameterized model to Linear × Qualitative interactions, where the qualitative variable may have 2 or 3 categories, and then describe how to modify the re-parameterized model to test moderating effects. To illustrate our new approach, we fit alternate models to social skills data on 438 participants in the National Institute of Child Health and Human Development Study of Early Child Care. The re-parameterized regression model had point and interval estimates of the crossover point that fell near the mean on the continuous environment measure. The disordinal form of the interaction supported 1 theoretical model-differential-susceptibility-over a competing model that predicted an ordinal interaction.

Bayesian Models for Categorical Data

Abstract: Preface. Chapter 1 Principles of Bayesian Inference. 1.1 Bayesian updating. 1.2 MCMC techniques. 1.3 The basis for MCMC. 1.4 MCMC sampling algorithms. 1.5 MCMC convergence. 1.6 Competing models. 1.7 Setting priors. 1.8 The normal linear model and generalized linear models. 1.9 Data augmentation. 1.10 Identifiability. 1.11 Robustness and sensitivity. 1.12 Chapter themes. References. Chapter 2 Model Comparison and Choice. 2.1 Introduction: formal methods, predictive methods and penalized deviance criteria. 2.2 Formal Bayes model choice. 2.3 Marginal likelihood and Bayes factor approximations. 2.4 Predictive model choice and checking. 2.5 Posterior predictive checks. 2.6 Out-of-sample cross-validation. 2.7 Penalized deviances from a Bayes perspective. 2.8 Multimodel perspectives via parallel sampling. 2.9 Model probability estimates from parallel sampling. 2.10 Worked example. References. Chapter 3 Regression for Metric Outcomes. 3.1 Introduction: priors for the linear regression model. 3.2 Regression model choice and averaging based on predictor selection. 3.3 Robust regression methods: models for outliers. 3.4 Robust regression methods: models for skewness and heteroscedasticity. 3.5 Robustness via discrete mixture models. 3.6 Non-linear regression effects via splines and other basis functions. 3.7 Dynamic linear models and their application in non-parametric regression. Exercises. References. Chapter 4 Models for Binary and Count Outcomes. 4.1 Introduction: discrete model likelihoods vs. data augmentation. 4.2 Estimation by data augmentation: the Albert-Chib method. 4.3 Model assessment: outlier detection and model checks. 4.4 Predictor selection in binary and count regression. 4.5 Contingency tables. 4.6 Semi-parametric and general additive models for binomial and count responses. Exercises. References. Chapter 5 Further Questions in Binomial and Count Regression. 5.1 Generalizing the Poisson and binomial: overdispersion and robustness. 5.2 Continuous mixture models. 5.3 Discrete mixtures. 5.4 Hurdle and zero-inflated models. 5.5 Modelling the link function. 5.6 Multivariate outcomes. Exercises. References. Chapter 6 Random Effect and Latent Variable Models for Multicategory Outcomes. 6.1 Multicategory data: level of observation and relations between categories. 6.2 Multinomial models for individual data: modelling choices. 6.3 Multinomial models for aggregated data: modelling contingency tables. 6.4 The multinomial probit. 6.5 Non-linear predictor effects. 6.6 Heterogeneity via the mixed logit. 6.7 Aggregate multicategory data: the multinomial-Dirichlet model and extensions. 6.8 Multinomial extra variation. 6.9 Latent class analysis. Exercises. References. Chapter 7 Ordinal Regression. 7.1 Aspects and assumptions of ordinal data models. 7.2 Latent scale and data augmentation. 7.3 Assessing model assumptions: non-parametric ordinal regression and assessing ordinality. 7.4 Location-scale ordinal regression. 7.5 Structural interpretations with aggregated ordinal data. 7.6 Log-linear models for contingency tables with ordered categories. 7.7 Multivariate ordered outcomes. Exercises. References. Chapter 8Discrete Spatial Data. 8.1 Introduction. 8.2 Univariate responses: the mixed ICAR model and extensions. 8.3 Spatial robustness. 8.4 Multivariate spatial priors. 8.5 Varying predictor effect models. Exercises. References. Chapter 9 Time Series Models for Discrete Variables. 9.1 Introduction: time dependence in observations and latent data. 9.2 Observation-driven dependence. 9.3 Parameter-driven dependence via DLMs. 9.4 Parameter-driven dependence via autocorrelated error models. 9.5 Integer autoregressive models. 9.6 Hidden Markov models. Exercises. References. Chapter 10 Hierarchical and Panel Data Models 10.1 Introduction: clustered data and general linear mixed models. 10.2 Hierarchical models for metric outcomes. 10.3 Hierarchical generalized linear models. 10.4 Random effects for crossed factors. 10.5 The general linear mixed model for panel data. 10.6 Conjugate panel models. 10.7 Growth curve analysis. 10.8 Multivariate panel data. 10.9 Robustness in panel and clustered data analysis. 10.10 APC and spatio-temporal models. 10.11 Space-time and spatial APC models. Exercises. References. Chapter 11 Missing-Data Models. 11.1 Introduction: types of missing data. 11.2 Density mechanisms for missing data. 11.3 Auxiliary variables. 11.4 Predictors with missing values. 11.5 Multiple imputation. 11.6 Several responses with missing values. 11.7 Non-ignorable non-response models for survey tabulations. 11.8 Recent developments. Exercises. References. Index.