Showing papers on "Ordinal regression published in 1999"

Support vector learning for ordinal regression

Abstract: We investigate the problem of predicting variables of ordinal scale. This task is referred to as ordinal regression and is complementary to the standard machine learning tasks of classification and metric regression. In contrast to statistical models we present a distribution independent formulation of the problem together with uniform bounds of the risk functional. The approach presented is based on a mapping from objects to scalar utility values. Similar to support vector methods we derive a new learning algorithm for the task of ordinal regression based on large margin rank boundaries. We give experimental results for an information retrieval task: learning the order of documents with respect to an initial query. Experimental results indicate that the presented algorithm outperforms more naive approaches to ordinal regression such as support vector classification and support vector regression in the case of more than two ranks.

Ordinal Data Modeling

Abstract: Review of Classical and Bayesian Inference.- Review of Bayesian Computation.- Regression Models for Binary Data.- Regression Models for Ordinal Data.- Analyzing Data from Multiple Raters.- Item Response Modeling.- Graded Response Models: A Case Study of Undergraduate Grade Data.

Extending Gower's general coefficient of similarity to ordinal characters

Abstract: Summary The possibilities of calculating similarity based on ordinal characters are evaluated by distinguishing subtypes of the ordinal scale. Multivariate analysis is most problematic when ordinal variables appear together with other scale types in the data. This difficulty is solved by extending Gower's general coefficient of similarity to ordinal data types, facilitating cluster analysis and multidimensional scaling. Two alternatives, a non-metric and a metric version, are offered. The modified formula implies that ordinal variables are equally weighted with the others, and that partially and fully ranked data are both applicable, due to the inherent standardisation procedure. A morphological data set derived for the moss genus Tortula illustrates the new approach.

A hierarchical latent variable model for ordinal data from a customer satisfaction survey with no answer responses

Abstract: We propose an item response theory model for ordinal customer satisfaction data where the probability of each response is a function of latent person and question parameters and of cutoffs for the ordinal response categories. This structure was incorporated into a Bayesian hierarchical model by Albert and Chib. We extend this formulation by modeling item nonresponse, coded as “no answer” (NA), as due to either lack of a strong opinion or indifference to the entire question. Because the probability of an NA is related to the latent opinion, the missing-data model is nonignorable. In our hierarchical Bayesian framework, prior means for the person and item effects are related to observed covariates. This structure supports model inferences about satisfaction of individual customers and about associations between customer characteristics and satisfaction levels or propensity to respond. We contrast this with exploratory and standard regression analyses that do not fully support these inferences. Our ...

Stock Evaluation Using a Preference Disaggregation Methodology

Abstract: This paper presents a real application of a multicriteria decision aid (MCDA) approach to portfolio selection based on preference disaggregation, using ordinal regression and linear programming (UTADIS method; UTilites Additives DIScriminantes). The additive utility functions that are derived through this approach have the extrapolation ability that any new alternative (share) can be easily evaluated and classified into one of several user-predefined groups. The procedure is illustrated with a case study of 98 stocks from the Athens stock exchange, using 15 criteria. The results are encouraging, indicating that the proposed methodology could be used as a tool for the analysis of the portfolio managers' preferences and choices. Furthermore, the comparison with multiple discriminant analysis (either using a stepwise procedure or not) illustrates the superiority of the proposed methodology over a well-known multivariate statistical technique that has been extensively used to study financial decision-making problems.

Generalized Estimating Equations for Ordinal Categorical Data: Arbitrary Patterns of Missing Responses and Missingness in a Key Covariate

Abstract: Summary. We propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables. The methods use ordinal regression models in conjunction with generalized estimating equations (GEEs). We extend the GEE methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses. We further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables. The approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables.

Probabilistic data clustering

Abstract: A component of a data clusterer is used to determine a conditional probability density of an object (data point) lying in a cluster. The object has a discrete ordinal attribute value within a finite range of attribute values. The conditional probability density for the discrete ordinal attribute is a function of an integral of a conditional probability function across a sub-range of the discrete ordinal attribute range of values, the sub-range comprising an upper bound and a lower bound bounding the discrete ordinal attribute value.

Modeling item nonresponse in questionnaires

Abstract: The statistical analysis of empirical questionnaire data can be hampered by the fact that not all questions are answered by all individuals. In this paper we propose a simple practical method to deal with such item nonresponse in case of ordinal questionnaire data, where we assume that item nonresponse is caused by an incomplete set of answers between which the individuals are supposed to choose. Our statistical method is based on extending the ordinal regression model with an additional category for nonresponse, and on investigating whether this extended model describes and forecasts the data well. We illustrate our approach for two questions from a questionnaire held amongst a sample of clients of a financial investment company.

Measuring change: mixed Markov models for ordinal panel data.

Abstract: In an analysis of longitudinal data it is important to distinguish between dependencies caused by within - and between - subject variability. This paper presents mixed Markov models for ordinal data that take into account both sources of variation. In addition, covariates that may capture differences among panel members and timespecific changes are also incorporated in the model. The model is derived by specifying an observation-driven process at the individual level and allowing for parametric or semi-parametric representations of random parameter variation across the units of analysis. As a result, the approach is well suited for modelling ordinal panel data with a large number of time points. In an application a three-week diary study is analysed to test hypotheses about the relationships between emotions and personality factors over time.

Classification to ordinal categories using a search partition methodology with an application in diabetes screening.

Abstract: A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obtained. The approach is applied to ordinal categories of glucose tolerance to discriminate between diabetes, impaired glucose tolerance and normal states. The results are compared with analysis by ordinal logistic regression and by classification trees.

Regression modeling of ordinal data with nonzero baselines.

Abstract: Summary. This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.

A general non-parametric approach to the analysis of ordinal categorical data

Abstract: This paper presents a general class of models for ordinal categorical data which can be specified by means of linear and/or log-linear equality and/or inequality restrictions on the (conditional) probabilities of a multi-way contingency table. Some special cases are models with ordered local odds ratios, models with ordered cumulative response probabilities, order-restricted row association and column association models, and models for stochastically ordered marginal distributions. A simple uni-dimensional Newton algorithm is proposed for obtaining the restricted maximum likelihood estimates. In situations in which there is some kind of missing data, this algorithm can be implemented in the M step of an EM algorithm. Computation of p-values of testing statistics is performed by means of parametric bootstrapping.

A stochastic model for the analysis of customer satisfaction: some theoretical aspects

Abstract: The paper deals with a model in which the overall customer satisfaction Y concerning a good or service, expressed by a respondent on an ordinal scale, is linked to the weights and ratings Wi* and Xi* , i=1, 2,...,K, that he respectively assigns on conventional ordinal scales to some of its specific aspects. It is assumed that the observed value of Y come from discretization of a continuous model....

Milieux de vie et intégration sociale: caractéristiques organisationnelles des résidences pour aîné(e)s et vie sociale des personnes âgées*

Abstract: This study examines the links between four organizational features of private housing for older persons (service level, perception of environmental control level, tolerance level of caregivers toward seniors and their input in decision making) and the social integration of seniors. This last variable is assessed according to four indicators: presence or absence of meaningful relationships, satisfaction with social life, feeling of loneliness and number of contacts with neighbours. The results obtained by analysing the logistic or ordinal regression and the odd ratio associate two of the four organizational variables studied to most of the social integration indicators irrespective of the subjects' vulnerability level. The two features are service level and perception of environmental control level.

The analysis of repeated ordinal data using latent trends

Abstract: This thesis presents methodology to analyse repeated ordered categorical data (repeated ordinal data), under the assumption that measurements arise as discrete realisations of an underlying (latent) continuous distribution. Two sets of estimation equations, called quasiestimation equations or QEEs, are presented to estimate the mean structure and the cutoff points which define boundaries between different categories. A series of simulation studies are employed to examine the quality of the estimation processes and of the estimation of the underlying latent correlation structure. Graphical studies and theoretical considerations are also utilised to explore the asymptotic properties of the correlation, mean and cutoff parameter estimates. One important aspect of repeated analysis is the structure of the correlation and simulation studies are used to look at the effect of correlation misspecification, both on the consistency of estimates and their asymptotical stability. To compare the QEEs with current methodology, simulations studies are used to analyse the simple case where the data are binary, so that generalised estimation equations (GEEs) can also be applied to model the latent trend. Again the effect of correlation misspecification will be considered. QEEs are applied to a data set consisting of the pain runners feel in their legs after a long race. Both ordinal and continuous responses are measured and comparisons between QEEs and continuous counterparts are made. Finally, this methodology is extended to the case when there are multivariate repeated ordinal measurements, giving rise to inter-time and intra-time correlations.