Showing papers on "Ordinal regression published in 2007"

Support Vector Ordinal Regression

Abstract: In this letter, we propose two new support vector approaches for ordinal regression, which optimize multiple thresholds to define parallel discriminant hyperplanes for the ordinal scales. Both approaches guarantee that the thresholds are properly ordered at the optimal solution. The size of these optimization problems is linear in the number of training samples. The sequential minimal optimization algorithm is adapted for the resulting optimization problems; it is extremely easy to implement and scales efficiently as a quadratic function of the number of examples. The results of numerical experiments on some benchmark and real-world data sets, including applications of ordinal regression to information retrieval, verify the usefulness of these approaches.

A comparison of three sets of criteria for determining the presence of differential item functioning using ordinal logistic regression

Abstract: Background Several techniques have been developed to detect differential item functioning (DIF), including ordinal logistic regression (OLR). This study compared different criteria for determining whether items have DIF using OLR.

Evaluating sampling strategies and logistic regression methods for modelling complex land cover changes

Abstract: Summary 1 The role of land cover change as a significant component of global change has become increasingly recognized in recent decades Large databases measuring land cover change, and the data which can potentially be used to explain the observed changes, are also becoming more commonly available When developing statistical models to investigate observed changes, it is important to be aware that the chosen sampling strategy and modelling techniques can influence results 2 We present a comparison of three sampling strategies and two forms of grouped logistic regression models (multinomial and ordinal) in the investigation of patterns of successional change after agricultural land abandonment in Switzerland 3 Results indicated that both ordinal and nominal transitional change occurs in the landscape and that the use of different sampling regimes and modelling techniques as investigative tools yield different results 4 Synthesis and applications Our multimodel inference identified successfully a set of consistently selected indicators of land cover change, which can be used to predict further change, including annual average temperature, the number of already overgrown neighbouring areas of land and distance to historically destructive avalanche sites This allows for more reliable decision making and planning with respect to landscape management Although both model approaches gave similar results, ordinal regression yielded more parsimonious models that identified the important predictors of land cover change more efficiently Thus, this approach is favourable where land cover change pattern can be interpreted as an ordinal process Otherwise, multinomial logistic regression is a viable alternative

Ageing, Learning, and Computer Technology in Australia

Abstract: Learning is an important aspect of active ageing, yet older people are not often included in discussions of the issue. Older people vary in their need, desire, and ability to learn, and this is evident in the context of technology. The focus of the data analysis for this paper was on determining the place of learning and technology in active ageing. The paper describes results from 2,645 respondents aged from 50 to 74 + years, in Australia, to a 178-item variable postal survey. The survey measured aspects of learning;, work; social, spiritual and emotional status; health; vision; home; life events; and demographics. There was also an open-ended question about being actively engaged in life. Ordinal regression analysis showed that interest in learning, keeping up to date, valuing communication, being younger, and being male are predictors of learning about technology. The results are at variance with an earlier analysis of our data which showed that women are generally more interested in learning. The open...

The effect of retirement on health: a panel analysis using data from the Swiss Household Panel.

Abstract: QUESTIONS UNDER STUDY Despite the importance of the relationship between retirement and health only a limited amount of empirical research has addressed this issue, particularly concerning physical health. This study examines whether retirement has a short-term influence on six health measures. METHODS Using data from the Swiss Household Panel from 1999 to 2003, we perform an ordinal regression on changes in health for each of the six health measures. RESULTS We found that retirement has no shortterm effect on the health of the large majority of individuals. Moreover, for those individuals whose health status did change, retirement had a primarily positive effect. This positive impact of retirement is mainly reflected by less frequent depression and anxiety, and by the lower degree to which health is an impediment in everyday activities. CONCLUSIONS The positive changes in health after retirement may be due to the cessation of work-related stress and to an increase in physical and leisure activities.

Aggregation of ordinal information

Abstract: Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.

An ensemble of Weighted Support Vector Machines for Ordinal Regression

Abstract: Instead of traditional (nominal) classification we investigate the subject of ordinal classification or ranking. An enhanced method based on an ensemble of Support Vector Machines (SVM's) is proposed. Each binary classifier is trained with specific weights for each object in the training data set. Experiments on benchmark datasets and synthetic data indicate that the performance of our approach is comparable to state of the art kernel methods for ordinal regression. The ensemble method, which is straightforward to implement, provides a very good sensitivity-specificity trade-off for the highest and lowest rank.

Time series from the ordinal viewpoint

Abstract: Ordinal time series analysis is a new approach to the investigation of long and complex time series, which bases on ordinal patterns describing the order relations between the values of a time series. In this paper we consider ordinal time series analysis from the conceptional viewpoint. In particular, we introduce ordinal processes as models for ordinal time series analysis and discuss the structure of ordinal pattern distributions obtained from them. Special emphasis is on the relation of ordinal time series analysis to symbolic dynamics and to a transformation extracting the whole ordinal information contained in a time series. Finally, we consider invariance properties of ordinal time series analysis.

Higher educated workers: better jobs but less satisfied?

Abstract: Purpose – The purpose of the paper is to clarify the mixed empirical results concerning the association between educational level and job satisfaction. It seeks to test whether the positive relationship between educational level and job satisfaction is caused by indicators of job quality.Design/methodology/approach – Three models are estimated. In the first model, the impact of the educational level on job satisfaction is examined using an ordinal regression analysis. The second model estimates the impact of the educational level on indicators of job quality, using the appropriate technique (OLS or binary logit). The third model reveals the “true” impact of the educational level on job satisfaction, when the job quality indicators are added as independent variables. Survey data on Flemish youth in their first job are used.Findings – The results show that higher educated workers are more satisfied than their lower educated counterparts, because they have a job of better quality. When one controls for all j...

Ordinal classification with decision rules

Abstract: We consider the problem of ordinal classification, in which a value set of the decision attribute (output, dependent variable) is finite and ordered. This problem shares some characteristics of multi-class classification and regression, however, in contrast to the former, the order between class labels cannot be neglected, and, in the contrast to the latter, the scale of the decision attribute is not cardinal. In the paper, following the theoretical framework for ordinal classification, we introduce two algorithms based on gradient descent approach for learning ensemble of base classifiers being decision rules. The learning is performed by greedy minimization of so-called threshold loss, using a forward stagewise additive modeling. Experimental results are given that demonstrate the usefulness of the approach.

Information seeking and intentions to have genetic testing for hereditary cancers in rural and Appalachian Kentuckians.

Abstract: Context: Research is limited regarding the potential of genetic testing for cancer risk in rural Appalachia. Purpose: This study examined perceptions of genetic testing in a population sample of Kentuckians, with a focus on Appalachian and rural differences. The goals were to examine cultural and psychosocial factors that may predict intentions to test for hereditary cancer, need for help with information seeking for decision making about genetic testing for hereditary cancer, and amount of help needed with information seeking for decision making about genetic testing for hereditary cancer in this population. Methods: Analysis of data from a general social survey of adults using random-digit dialing in Kentucky (N = 882). Findings: An ordinal regression found that younger age, having a family history of cancer, and greater worry predicted greater intentions to seek genetic testing. A logistic regression found that having more education, excellent subjective knowledge of genetics, and less worry about cancer predicted less need for help in seeking information about testing. An ordinal regression found that less subjective knowledge of genetics and greater worry predicted greater amount of help needed. Conclusions: Additional counseling to explain limitations of genetic testing may be needed. Further, those with less knowledge about genetics and more worry about hereditary cancer may have greater need for help with information seeking for decision making, a need that may be further exacerbated by the lack of medical professionals, particularly genetic counselors, who may provide information about genetic testing in rural, Appalachian Kentucky.

A penalized latent class model for ordinal data.

Abstract: Latent class models provide a useful framework for clustering observations based on several features. Application of latent class methodology to correlated, high-dimensional ordinal data poses many challenges. Unconstrained analyses may not result in an estimable model. Thus, information contained in ordinal variables may not be fully exploited by researchers. We develop a penalized latent class model to facilitate analysis of high-dimensional ordinal data. By stabilizing maximum likelihood estimation, we are able to fit an ordinal latent class model that would otherwise not be identifiable without application of strict constraints. We illustrate our methodology in a study of schwannoma, a peripheral nerve sheath tumor, that included 3 clinical subtypes and 23 ordinal histological measures.

Random effects modeling approaches for estimating ROC curves from repeated ordinal tests without a gold standard.

Abstract: Estimating diagnostic accuracy without a gold standard is an important problem in medical testing. Although there is a fairly large literature on this problem for the case of repeated binary tests, there is substantially less work for the case of ordinal tests. A noted exception is the work by Zhou, Castelluccio, and Zhou (2005, Biometrics 61, 600-609), which proposed a methodology for estimating receiver operating characteristic (ROC) curves without a gold standard from multiple ordinal tests. A key assumption in their work was that the test results are independent conditional on the true test result. I propose random effects modeling approaches that incorporate dependence between the ordinal tests, and I show through asymptotic results and simulations the importance of correctly accounting for the dependence between tests. These modeling approaches, along with the importance of accounting for the dependence between tests, are illustrated by analyzing the uterine cancer pathology data analyzed by Zhou et al. (2005).

A Risk Minimization Principle for a Class of Parzen Estimators

Abstract: This paper1 explores the use of a Maximal Average Margin (MAM) optimality principle for the design of learning algorithms. It is shown that the application of this risk minimization principle results in a class of (computationally) simple learning machines similar to the classical Parzen window classifier. A direct relation with the Rademacher complexities is established, as such facilitating analysis and providing a notion of certainty of prediction. This analysis is related to Support Vector Machines by means of a margin transformation. The power of the MAM principle is illustrated further by application to ordinal regression tasks, resulting in an O(n) algorithm able to process large datasets in reasonable time.

Latent-variable models for longitudinal data with bivariate ordinal outcomes.

Abstract: We use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes, and then extend the model to allow for longitudinal data. Specifically, we relate the observed ordinal outcomes using threshold values to a bivariate latent variable, which is then modelled as a linear mixed model. Random effects terms are used to tie all together repeated observations from the same subject. The cross-sectional association between the two outcomes is modelled through the correlation coefficient of the bivariate latent variable, conditional on random effects. Assuming conditional independence given random effects, the marginal likelihood, under the missing data at random assumption, is approximated using an adaptive Gaussian quadrature for numerical integration. The model provides fixed effects parameters that are subject-specific, but retain the population-averaged interpretation when properly scaled. This is particularly well suited for the situation in which population comparisons and individual level contrasts are of equal importance. Data from a psychiatric trial, the Fluvoxamine (an antidepressant drug) study, are used to illustrate the methodology.

A fast algorithm for learning large scale preference relations

Abstract: We consider the problem of learning the ranking function that maximizes a generalization of the Wilcoxon-Mann-Whitney statistic on training data. Relying on an 2-exact approximation for the error-function, we reduce the computational complexity of each iteration of a conjugate gradient algorithm for learning ranking functions from O(m2), to O(m), where m is the size of the training data. Experiments on public benchmarks for ordinal regression and collaborative filtering show that the proposed algorithm is as accurate as the best available methods in terms of ranking accuracy, when trained on the same data, and is several orders of magnitude faster.

Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model

Abstract: In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the case of the generalized stereotype model this includes category-specific random effects due to individual differences in response style. But unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model. This paper discusses the specification, interpretation, identification, and estimation of generalized stereotype models. Two applications are provided for illustration.

Do determinants of online shopping differ for personal shoppers and professional shoppers

Abstract: Purpose – Individuals use the web for shopping for both personal and professional objectives. The purpose of this paper is to show that the demographic profile of individuals who shop online for personal reasons is different from that of those who shop for professional reasons.Design/methodology/approach – Based on marketing literature, hypotheses were generated regarding the relationships between proclivity to purchase online and demographics. The data were collected through online surveys, and the hypotheses tested with an ordinal regression model.Findings – This research indicated that individuals with children, high incomes, and large internet experience are more likely to shop online for personal purposes and younger men with large internet experience are more likely to shop online for professional purposes.Research limitations/implications – One of the limitations of this study is that it focuses on only the demographic determinants, and ignores others, such as reputation and size, service quality, ...

Application of Prediction Analysis to Cross Classifications of Ordinal Data

Abstract: Prediction analysis (PA) of cross classifications is characterized as a method for the analysis of local prediction hypotheses, that is, hypotheses that link particular predictor states to particular states of criteria. To evaluate the success of a prediction, PA compares the observed with an expected frequency distribution. The latter is estimated under the assumption of independence between predictors and criteria. When predictors of criteria have ordinal categories, the success of a prediction hypothesis is overestimated if there is a regression of the cell frequencies on the ranks of the variable categories. Using the method of log-linear models, it is shown how ordinal categories can be taken into account in PA. Numerical examples are given from the areas of cognitive development and drug research.

Focused crawling with scalable ordinal regression solvers

Abstract: In this paper we propose a novel, scalable, clustering based Ordinal Regression formulation, which is an instance of a Second Order Cone Program (SOCP) with one Second Order Cone (SOC) constraint. The main contribution of the paper is a fast algorithm, CB-OR, which solves the proposed formulation more eficiently than general purpose solvers. Another main contribution of the paper is to pose the problem of focused crawling as a large scale Ordinal Regression problem and solve using the proposed CB-OR. Focused crawling is an efficient mechanism for discovering resources of interest on the web. Posing the problem of focused crawling as an Ordinal Regression problem avoids the need for a negative class and topic hierarchy, which are the main drawbacks of the existing focused crawling methods. Experiments on large synthetic and benchmark datasets show the scalability of CB-OR. Experiments also show that the proposed focused crawler outperforms the state-of-the-art.

Log-linear non-uniform association models for agreement between two ratings on an ordinal scale.

Abstract: In agreement studies, when objects are rated independently by two raters (or twice by the same rater), an association between their ratings on two categories arises, reflecting the distinguishability of these two categories for these raters. When ratings are performed on an ordinal scale, this association between ratings on two categories increases when the distance between these categories increases on the ordinal scale. Goodman's log-linear models derived for the analysis of agreement between two raters on an ordinal scale assume that distinguishabilities between adjacent categories are either constant, or a priori fixed. Log-non-linear models that allow variations of the distinguishabilities between adjacent categories along the scale, may lead to difficulties in parameter estimation. This paper describes a new class of log-linear non-uniform association models. These models extend the log-linear uniform association model by allowing variations of distinguishability between adjacent categories (along the scale). These new models are used to analyse ordinal agreement between dermatologists when assessing the severity of different cutaneous signs of ageing on women faces.

An Ordinal Regression Model using Dealer Satisfaction Data

Abstract: This article analyses dealer satisfaction data in the agricultural technology market in Germany. The dealers could rate their suppliers in the ?overall satisfaction? and in 38 questions which can be summarized in 8 dimensions. An ordinal regression model which is also known as the proportional odds model is used to analyse the ordinal scaled rating of the dealers. The ordinal regression model is a well examined method in econometric theory, but many authors prefer using a linear regression model due to better interpretation, even the assumptions of a linear regression do not fit the data. Since the estimated coefficients of an ordinal regression model can not be properly interpreted we show other methods for a better insight of the relationship of the dealer satisfaction and the influencing variables. These methods are easy to use and it is recommended to list some of them in empirical papers.

An ordinal characterization of the linear opinion pool

Abstract: Given a collection of individual ordinal probabilities on a finite state space, we discuss an ordinal condition that is necessary and sufficient for an ordinal probability to be represented as a weighted average of probability representations of the individual probabilities. We also give necessary and sufficient conditions for when such an ordinal probability can be represented as an unweighted average of probability representations.