Ordinal regression

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

SPSS 14.0 Advanced Statistical Procedures Companion

Abstract: SPSS 14.0 Advanced Statistical Procedures Companion: Chapters 1. Model Selection in Loglinear Analysis. Model formulation parameters in saturated models hypothesis testing convergence goodness-of-fit tests hierarchical models generating classes model selection with backward elimination. 2. Logit Loglinear Analysis. Dichotomous logit model loglinear representation parameter estimates goodness-of-fit statistics measures of dispersion and association polychotomous logit model interpreting parameters examining residuals introducing covariates. 3. Multinomial Logistic Regression. Baseline logits likelihood-ratio tests for models and individual effects evaluating the model calculating predicted probabilities the classification table goodness-of-fit tests residuals pseudo R-square measures overdispersion model selection matched case-control studies. 4. Ordinal Regression. Modeling cumulative counts parameter estimates testing for parallel lines model fit observed and expected counts measures of strength of association classifying cases link functions fitting a heteroscedastic probit model fitting location and scale parameters. 5. Probit Regression. Probit and logit response models confidence intervals for effective dosages comparing groups comparing relative potencies estimating the natural response rate multiple stimuli. 6. Kaplan-Meier Survival Analysis. Calculating survival time estimating the survival function, the conditional probability of survival, and the cumulative probability of survival plotting survival functions comparing survival functions stratified comparisons. 7. Life Tables. Calculating survival probabilities assumptions observations lost to follow-up plotting survival functions comparing survival functions. 8. Cox Regression. The model proportional hazards assumption coding categorical variables interpreting the regression coefficients baseline hazard and cumulative survival rates global tests of the model checking the proportional hazards assumption stratification log-minus-log survival plot identifying influential cases examining residuals partial (Schoenfeld) residuals martingale residuals variable-selection methods time-dependent covariates specifying a time-dependent covariate calculating segmented time-dependent covariates testing the proportional hazards assumption with a time-dependent covariate fitting a conditional logistic regression model. 9. Variance Components. Factors, effects, and models model for one-way classification estimation methods negative variance estimates nested design model for two-way classification univariate repeated measures analysis using a Mixed Models Approach distribution assumptions estimation methods. 10. Linear Mixed Models. Background Unconditional random-effects models hierarchical models random-coefficient model model with school-level and individual-level covariates three-level hierarchical model repeated measurements selecting a residual covariance structure. 11. Nonlinear Regression. The nonlinear model transforming nonlinear models intrinsically nonlinear models fitting a logistic population growth model finding starting values approximate confidence intervals for the parameters bootstrapped estimates starting values from previous analysis linear approximation computational issues common models for nonlinear regression specifying a segmented model. 12. Two-Stage Least-Squares Regression. Demand-price-income economic model estimation with ordinary least squares feedback and correlated errors estimation with two-stage least squares. 13. Weighted Least-Squares Regression. Diagnosing the problem estimating weights examining the log-likelihood function the WLS solution estimating weights from replicates diagnostics from the linear regression procedure. 14. Multidimensional Scaling. Data, models, and multidimensional scaling analysis nature of data analyzed in MDS measurement level of data shape of data conditionality of data missing data multivariate data classical MDS Euclidean model details of CMDS Replicated MDS Weighted MDS geometry of the weighted Euclidean model algebra of the weighted Euclidean model matrix algebra of the weighted Euclidean model Weirdness index flattened weights.

Estimating Functions of Mixed Ordinal and Categorical Variables Using Adaptive Splines

Abstract: : Multivariate adaptive regression splines (MARS) is a methodology for nonparametrically estimating (and interpreting) general functions of a high-dimensional argument given (usually noisy) data. Its basic underlying assumption is that the function to be estimated is locally relatively smooth where smoothness is adaptively defined depending on the local characteristics of the function. The usual definitions of smoothness do not apply to variables that assume unorderable categorical values. After a brief review of the MARS strategy for estimating functions of ordinal variables, alternative concepts of smoothness appropriate for categorical variables are introduced. These concepts lead to procedures that can estimate and interpret functions of many categorical variables, as well as those involving (many) mixed ordinal and categorical variables. They also provide a natural mechanism for modeling and predicting in the presence of missing predictor values (ordinal or categorical).

Regression: The Apple Does Not Fall Far From the Tree.

Abstract: Researchers and clinicians are frequently interested in either: (1) assessing whether there is a relationship or association between 2 or more variables and quantifying this association; or (2) determining whether 1 or more variables can predict another variable. The strength of such an association is mainly described by the correlation. However, regression analysis and regression models can be used not only to identify whether there is a significant relationship or association between variables but also to generate estimations of such a predictive relationship between variables. This basic statistical tutorial discusses the fundamental concepts and techniques related to the most common types of regression analysis and modeling, including simple linear regression, multiple regression, logistic regression, ordinal regression, and Poisson regression, as well as the common yet often underrecognized phenomenon of regression toward the mean. The various types of regression analysis are powerful statistical techniques, which when appropriately applied, can allow for the valid interpretation of complex, multifactorial data. Regression analysis and models can assess whether there is a relationship or association between 2 or more observed variables and estimate the strength of this association, as well as determine whether 1 or more variables can predict another variable. Regression is thus being applied more commonly in anesthesia, perioperative, critical care, and pain research. However, it is crucial to note that regression can identify plausible risk factors; it does not prove causation (a definitive cause and effect relationship). The results of a regression analysis instead identify independent (predictor) variable(s) associated with the dependent (outcome) variable. As with other statistical methods, applying regression requires that certain assumptions be met, which can be tested with specific diagnostics.

Joint modeling of longitudinal ordinal data and competing risks survival times and analysis of the NINDS rt-PA stroke trial.

Abstract: Existing joint models for longitudinal and survival data are not applicable for longitudinal ordinal outcomes with possible non-ignorable missing values caused by multiple reasons We propose a joint model for longitudinal ordinal measurements and competing risks failure time data, in which a partial proportional odds model for the longitudinal ordinal outcome is linked to the event times by latent random variables At the survival endpoint, our model adopts the competing risks framework to model multiple failure types at the same time The partial proportional odds model, as an extension of the popular proportional odds model for ordinal outcomes, is more flexible and at the same time provides a tool to test the proportional odds assumption We use a likelihood approach and derive an EM algorithm to obtain the maximum likelihood estimates of the parameters We further show that all the parameters at the survival endpoint are identifiable from the data Our joint model enables one to make inference for both the longitudinal ordinal outcome and the failure times simultaneously In addition, the inference at the longitudinal endpoint is adjusted for possible non-ignorable missing data caused by the failure times We apply the method to the NINDS rt-PA stroke trial Our study considers the modified Rankin Scale only Other ordinal outcomes in the trial, such as the Barthel and Glasgow scales, can be treated in the same way

A mixed ordinal location scale model for analysis of Ecological Momentary Assessment (EMA) data.

Abstract: Mixed-effects logistic regression models are described for analysis of longitudinal ordinal outcomes, where observations are observed clustered within subjects. Random effects are included in the model to account for the correlation of the clustered observations. Typically, the error variance and the variance of the random effects are considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In this article, we describe how covariates can influence these variances, and also extend the standard logistic mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their responses. Additionally, we allow the random effects to be correlated. We illustrate application of these models for ordinal data using Ecological Momentary Assessment (EMA) data, or intensive longitudinal data, from an adolescent smoking study. These mixed-effects ordinal location scale models have useful applications in mental health research where outcomes are often ordinal and there is interest in subject heterogeneity, both between- and within-subjects.