Showing papers on "Ordinal regression published in 1997"
TL;DR: A synthesized review of generalized linear regression models for analysing ordered responses and the formulation of ordinal models, interpretation of model parameters, and their implications for epidemiological research are presented.
Abstract: Background Epidemiologists are often interested in estimating the risk of several related diseases as well as adverse outcomes, which have a natural ordering of severity or certainty. While most investigators choose to model several dichotomous outcomes (such as very low birthweight versus normal and moderately low birthweight versus normal), this approach does not fully utilize the available information. Several statistical models for ordinal responses have been proposed, but have been underutilized. In this paper, we describe statistical methods for modelling ordinal response data, and illustrate the fit of these models to a large database from a perinatal health programme. Methods Models considered here include (1) the cumulative logit model, (2) continuation-ratio model, (3) constrained and unconstrained partial proportional odds models, (4) adjacent-category logit model, (5) polytomous logistic model, and (6) stereotype logistic model. We illustrate and compare the fit of these models on a perinatal database, to study the impact of midline episiotomy procedure on perineal lacerations during labour and delivery. Finally, we provide a discussion on graphical methods for the assessment of model assumptions and model constraints, and conclude with a discussion on the choice of an ordinal model. The primary focus in this paper is the formulation of ordinal models, interpretation of model parameters, and their implications for epidemiological research. Conclusions This paper presents a synthesized review of generalized linear regression models for analysing ordered responses. We recommend that the analyst performs (i) goodness-of-fit tests and an analysis of residuals, (ii) sensitivity analysis by fitting and comparing different models, and (iii) by graphically examining the model assumptions.
519 citations
TL;DR: It is concluded that ordinal regression is a tool that is powerful, simple to use, and produces an interpretable parameter that summarizes the effect between groups over all levels of the outcome.
327 citations
TL;DR: In this paper, a model for longitudinal ordinal data with non-random dropout was proposed, which combines the multivariate Dale model with a logistic regression model for dropout.
Abstract: A model is proposed for longitudinal ordinal data with nonrandom drop-out, which combines the multivariate Dale model for longitudinal ordinal data with a logistic regression model for drop-out Since response and drop-out are modelled as conditionally independent given complete data, the resulting likelihood can be maximised relatively simply, using the EM algorithm, which with acceleration is acceptably fast and, with appropriate additions, can produce estimates of precision The approach is illustrated with an example Such modelling of nonrandom drop-out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense, and the conclusions cannot be regarded as necessarily robust The main role of such modelling may be as a component of a sensitivity analysis
202 citations
TL;DR: In this article, the authors present a general framework for associating value or worth with ordinal ranks, and develop models for deriving a consensus based on this framework, showing that the lp distance models using this framework are equivalent to the conventional ordinal models for any p ⩾ 1.
105 citations
23 Apr 1997
TL;DR: A set of alternative discretization methods are described and, based on the experimental results, the need for a search-based approach to choose the best method is justified and the accuracy benefits of adding misclassification costs are revealed.
Abstract: We present a methodology that enables the use of classification algorithms on regression tasks. We implement this method in system RECLA that transforms a regression problem into a classification one and then uses an existent classification system to solve this new problem. The transformation consists of mapping a continuous variable into an ordinal variable by grouping its values into an appropriate set of intervals. We use misclassification costs as a means to reflect the implicit ordering among the ordinal values of the new variable. We describe a set of alternative discretization methods and, based on our experimental results, justify the need for a search-based approach to choose the best method. Our experimental results confirm the validity of our search-based approach to class discretization, and reveal the accuracy benefits of adding misclassification costs.
34 citations
TL;DR: In this article, an estimation procedure for a class of threshold models for ordinal data is presented for a practical problem involving damage to potato tubers and with data from animal breeding and medical research from the literature.
Abstract: An estimation procedure will be presented for a class of threshold models for ordinal data. These models may include both fixed and random effects with associated components of variance on an underlying scale. The residual error distribution on the underlying scale may be rendered greater flexibility by introducing additional shape parameters, e.g. a kurtosis parameter or parameters to model heterogeneous residual variances as a function of factors and covariates. The estimation procedure is an extension of an iterative re-weighted restricted maximum likelihood procedure, originally developed for generalized linear mixed models. This procedure will be illustrated with a practical problem involving damage to potato tubers and with data from animal breeding and medical research from the literature.
28 citations
01 Jan 1997
TL;DR: In this article, a model for constructing quadratic and polynomial objective functions in n target variables from interviewing an expert is considered, where the person interviewed is presented a set of incomplete alternatives (vectors of target variables with one coordinate not fixed) and is asked to complete these alternatives (to adjust these coordinates) to the end of making the given alternatives equivalent in preference to some reference vector.
Abstract: A model for constructing quadratic and polynomial objective functions in n target variables from interviewing an expert is considered The person interviewed is presented a set of incomplete alternatives (vectors of target variables with one coordinate not fixed) and is asked to complete these alternatives (to adjust these coordinates) to the end of making the given alternatives equivalent in preference to some reference vector Then an indifference hypersurface is fitted to the equivalent vectors, thus determining the objective function on the whole of ℝn The data required for the construction are ordinal, simplest, and minimal It is proved that the resulting ordinal preference is independent of the cardinal utility scale used in intermediate computations Besides formal properties of the model and its regression-like extensions, computer experiments on constructing an objective function of German economic policy in four target variables (inflation, unemployment, GNP growth, and public debt) are briefly reported for illustration
19 citations
05 Jan 1997
TL;DR: It is shown that ordinal representations of distance matrices can be found in O(n{sup 2}log{Sup 2} n) time where n is the number of species and Ordinal representations are shown to be unique, when they exist.
Abstract: In this paper we present four results on the inference of evolutionary trees from ordinal information. An evolutionary tree T, or phylogeny, is an ordinal representation of a distance matrix , for all species a, b, c and d under consideration. In particular, we show that (1) Ordinal representations of distance matrices can be found in O(n{sup 2}log{sup 2} n) time where n is the number of species. Ordinal representations are shown to be unique, when they exist. (3) Determining if there is an ordinal representation for an incomplete distance matrix, a situation which arises in evolutionary studies, is NP-complete. (3) Finding a phylogeny that best fits a distance matrix containing ordinal errors is NP-complete. (4) Under reasonable conditions, a weighted ordinal representation of a distance matrix can be obtained in polynomial time.
12 citations
01 Dec 1997
TL;DR: In this article, the authors compared the performance of neural networks to those from ordinal logit models for a multi-state response variable and found that neural networks produce higher overall classification rates than ordinal logsit models, but do not more accurately classify distressed firms.
Abstract: In this study we compared the classification accuracy rates of neural networks to those from ordinal logit models for a multi-state response variable. The results indicate that with the multi-state response variable, neural networks produce higher overall classification rates than ordinal logit models, but do not more accurately classify distressed firms. As a result, we can not clearly state that neural networks are superior to regression when predicting more than one level of financial distress.
7 citations
DOI•
01 Jan 1997
TL;DR: In this article, a class of multivariate regression models for ordinal response variables in which the coefficients of the explanatory variables are allowed to vary as smooth functions of other variables is presented.
Abstract: We present a class of multivariate regression models for ordinal response variables in which the coefficients of the explanatory variables are allowed to vary as smooth functions of other variables. In the first part of the paper we consider a semiparametric cumulative regression model for a single ordinal outcome variable. A penalized maximum likelihood approach for estimating functions and parameters of interest is described. In the second part we explore a semiparametric marginal modeling framework appropriate for correlated ordinal responses. We model the marginal response probabilities and pairwise association structure by two semiparametric regressions. To estimate the model we derive an algorithm which is based on penalized generalized estimating equations. This nonparametric approach allows to estimate the marginal model without specifying the entire distribution of the correlated response. The methods are illustrated by two applications concerning the attitude toward smoking restrictions in the workplace and the state of damage in a Bavarian forest district.
6 citations
01 Jan 1997
TL;DR: In this paper, a class ordinal regression models in which the link function has scale parameters that may be estimated along with the regression parameters is described. But this model is not suitable for group level categorical responses.
Abstract: This paper describes a class ordinal regression models in which the link function has scale parameters that may be estimated along with the regression parameters. One motivation is to provide a plausible model for group level categorical responses. In this case a natural class of scaled link functions is obtained by treating the group level responses as threshold averages of possible correlated latent individual level variables. We find scaled link functions also arise naturally in other circumstances. Our methodology is illustrated through environmental risk assessment data where (correlated) individual level responses and group level responses are mixed.
Book•
01 Jan 1997
TL;DR: A meta-modelling approach to estimate the impact of Risk Factors on the Disease Load in a Population and some issues in the Comparison of Diagnostic Tests from a Paired Experiment are discussed.
Abstract: Section 1: Data Analysis and Classification.- Probability Models for Convex Clusters.- Multidimensional Scaling: Analyzing Multineuronal Spike Patterns.- Fixed Point Clusters and Their Relation to Stochastic Models.- A Metric Approach for Ordinal Regression.- Graphical Stability of Data Analysing Software.- Recent Developments in Three-Way Data Analysis: A Showcase of Methods and Examples.- A Hybrid Global Optimization Algorithm for Multidimensional Scaling.- Ordinal Regression.- Numerical Algorithms for Multidimensional Scaling.- High Dimensional Clustering Using Parallel Coordinates and the Grand Tour.- Section 2: Neural Networks and Pattern Recognition.- A Symbolic Representation for Patterns in Time Series Using Definitive Clause Grammars.- Neural Networks: A Statistician's (Possible) View.- Dynamic Supervised Learning: Some Basic Issues and Application Aspects.- A Hierarchical Neural Network Model for Pattern Recognition.- Section 3: Statistical Models and Methods.- Markov Random Field Models with Spatially Varying Coefficients.- Distribution of a Likelihood Ratio Statistic for Spatial Disease Clusters.- Biased Methods of Discrimination in High Dimensions: A Comparative Assessment.- A One-Step Optimization Procedure for the ARFIMA Processes.- GARCH Models with Outliers.- Minimum Volume Sets in Statistics: Recent Developments.- Fusion of Data Sets in Multivariate Linear Regression with Errors-in- Variables.- Discriminant Analysis for Directional Data Exemplified in a Concrete Case.- Combination of Tests and Sequential Classification.- Classes of Influential Observations.- Bayesian Non-Linear Latent Variable Models.- Section 4: Information Systems: Design and Implementation.- Case Based Software Engineering CBSE - The Example of a Store Control System.- Optimization in Probabilistic Logic for Decision Support Systems.- Learning Strategies for Managing New and Innovative Products.- Interoperable Database Systems.- Consistent Completion of Incomplete Data Objects.- Towards a Case-Based Assistant for the Conceptual Modelling of Information Systems.- Foundational Aspects of Knowledge-Based Information Systems in Scientific Domains.- Section 5: Text Analysis and Information Retrieval.- A Planning-Based Approach to Intelligent Information Retrieval in Text Databases.- 3D-Navigation in Virtual Information Spaces: From Text-Based Retrieval to Cognitive User Interaction.- A Note on Intelligent Information Retrieval Tools in the World Wide Web.- Computer-Aided Methods for Typification in Qualitative Social Research.- Classification of Text Analysis Software.- Computer Aided Text Analysis and Typology Construction.- Rotwang's Children: Information Ecology and the Internet.- Network Approaches in Text Analysis.- Qualitative Software and Analysis Structures: Solving Problems or Creating Them?.- Computer Tools for Grounded Theory: Introducing ATLAS/ti for Windows 95.- Section 6: Applications in Medicine.- Some Issues in the Comparison of Diagnostic Tests from a Paired Experiment.- Formal Modeling of Medical Concept Systems Considering Part-Whole Relations.- Classification of Oligodendrogliomas Using Neural Networks.- Statistical Methods to Estimate the Impact of Risk Factors on the Disease Load in a Population.- Neural Networks for Classification of Image Data in Quantitative Pathology.- Variations on the Shapley Solution for Partitioning Risks in Epidemiology.- Generalized Regression Trees Applied to Longitudinal Nutritional Survey Data.- Conceptual Complexity in Biomedical Terminologies: The UMLS Approach.- Sun Protection of Children: Changing Patterns of Preventive Knowledge and Behaviour.- A Natural Language Understanding System for Knowledge-Based Analysis of Medical Texts.- On the Development and Validation of Classification Schemes in Survival Data.- Use of Crossvalidation to Assess Diagnostic Classification Schemes of Atopic Dermatitis.- Differences of Representing a Conventional Classification by the Compositional Concept Representation Languages BERNWARD and GRAIL.- The Freiburg Center of Data Analysis and Model Building (FDM): An Interim Report about an Interdisciplinary Coorperation.- Realization of a Medical Data Dictionary in a Relational Database Management System.- Section 7: Applications in Economics and Social Sciences.- Two-Mode Overlapping Clustering With Applications to Simultaneous Benefit Segmentation and Market Structuring.- An Application of Two-Mode Classification to Analyze the Statistical Software Market.- Correspondence Analysis of Square Tables, with an Application to Social Mobility.- Identifying Benchmarking-Partners Using Two-Mode Classification.- Supporting the Search for Final Scenarios by the Fuzzy-C-Means Algorithm.- Two-Mode Classification in Advertising Research.- Neural Networks as Instruments for Automotive Market Segmentation.- Section 8: Applications in Archaeology, Biology, Linguistics and Dialectometry.- Seriation in Archaeology: Modelling, Methods and Prior Information.- Probabilistic Aspects of Sequence Repeats and Sequencing by Hybridization.- On the Equivalence of Two Tree Mapping Measures.- Deriving Grammars from Large Corpora.- Investigation of the Language in Germany and Austria Using Statistical Methods.- Current Trends in Dialectometry: The Handling of Synonym Feature Realizations.- Interactive Graphical Analysis of Regional Dialects.- Subject Index (including List of Authors).
01 Jan 1997
TL;DR: The main focus of this paper is planning, implementation, and evaluation of a survey on ordinal preferences according to the model by Gruber and Tangian and some extensions of the used method for estimating quadratic objective functions are proposed.
Abstract: The main focus of this paper is planning, implementation, and evaluation of a survey on ordinal preferences according to the model by Gruber and Tangian (elsewhere in this volume). A questionnaire to reveal preferences for the economic situation in Sachsen-Anhalt (a new state of the Federal Republic of Germany with the capital Magdeburg) has been developed and given to members of the state parliament. The quadratic objective functions estimated from the data collected have been used to evaluate the economic development in Sachsen-Anhalt. The results are discussed and some extensions of the used method for estimating quadratic objective functions are proposed.
01 Jan 1997
TL;DR: The necessary steps to estimate an ordered regression model and how to produce and interpret predicted probabilities are explained and illustrated with SUIVey data from a two county area in california (the Inland Empire).
Abstract: Most survey research regarding public opinion (from product satisfaction to presidential approval) provide ordinal response data. There are many ways to analyze ordinal outcomes using SAS but one of the most useful methods is PROC PROBIT. Although this procedure is comprehensive, the coefficients cannot be interpreted directly because they reflect the arbitrary assumptions used in identifying the model. Instead, predicted probabilities and partial and discrete change in probabilities should be used to interpret the relationship between independent ciePendent variables. Unfortunately calculating these probabilities using PROC PROBIT is not an intuitive process and the estimated intercept and thresholds are often different from other statistical packages because of different idenlifY:ing assumptions. This paper will explain the necessary steps to estimate an ordered regression model and how to produce and interpret predicted probabilities. These methods are illustrated with SUIVey data from a two county area in california (the Inland Empire). ·
01 Jan 1997
TL;DR: In this paper, a metric approach for the regression of ordinal variables is presented, where the problem of independent, ordinal variable with a dependent variable that is a metric scale is analyzed.
Abstract: This paper presents a metric approach for the regression of ordinal variables. In contrast to most other studies, the problem of independent, ordinal variables with a dependent variable that is a metric scale is analyzed. For this situation, some properties of the estimated parameters of the model are described.