Showing papers on "Ordinal regression published in 1983"

A Survey of Strategies for Modeling Cross-Classifications Having Ordinal Variables

Abstract: A survey is given of the main strategies for modeling cross-classifications that contain ordinal variables. Models are described for two-way tables in which one or both classifications are ordered and for multidimensional tables in which at least one classification is ordered. Primary emphasis is given to construction, interpretation, and implications of loglinear and logit models.

Testing Marginal Homogeneity for Ordinal Categorical Variables

Abstract: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. International Biometric Society is collaborating with JSTOR to digitize, preserve and extend access to Biometrics. SUMMARY The standard chi square tests of marginal homogeneity take no account of possible category ordering. We describe several strategies that make use of category order and which tend to yield more powerful tests for certain common alternatives.

Association Models for Multi-Dimensional Cross-Classifications of Ordinal Variables

Abstract: Models are formulated for describing associations among ordinal variables in multidimensional tables.Uniform association and uniform interaction models occur as special cases in which equal-interval scores are assigned to levels of the variables.The models described are extensions of ones proposed by Goodman (1979).

Linear Models Methods for Some Rank Function Analyses of Ordinal Categorical Data

Abstract: This paper is concerned with the analysis of ordinal data through linear models for rank function measures.Primary attention is directed at pairwise Mann-Whitney statistics for which dimension reduction is managed by use of a Bradley-Terry log-linear structure.The nature of linear models for such quantities is contrasted with that for mean ranks (or ridits).Aspects of application are illustrated with an example for which results of other methods are also given.

Methods for incorporating ordinal information into analysis of variance: Generalizations of one‐tail tests

Abstract: Methods for incorporating ordinal assumptions into the analysis of the means of k treatments (k > 2) are critically reviewed. These methods are examined under three headings: (1) Global: statistics that give an overall assessment of the presence of a trend in the data (e.g. linear and isotonic regression); (2) Multiple comparisons: statistics based on the repetition (explicit or implicit) of comparisons between pairs of treatments; (3) Joint probability: two statistics are computed, one giving an overall assessment of the differences between the means, the other assessing the specifically ordinal information in the data; the joint significance level of these two statistics is then determined. Numerical examples of all the methods are provided.

Ordinal data, ordered scale points, and order statistics

Abstract: This paper concerns ordinal responses. An ordered Dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories. Associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable. The psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference. An example relates the skewness of a latent variable to the proportional odds and proportional hazards models of McCullagh [1980].