Showing papers on "Ordinal regression published in 2003"

A general class of latent variable models for ordinal manifest variables with covariate effects on the manifest and latent variables

Abstract: Previous work on a general class of multidimensional latent variable models for analysing ordinal manifest variables is extended here to allow for direct covariate effects on the manifest ordinal variables and covariate effects on the latent variables. A full maximum likelihood estimation method is used to estimate all the model parameters simultaneously. Goodness-of-fit statistics and standard errors are discussed. Two examples from the 1996 British Social Attitudes Survey are used to illustrate the methodology.

On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style

Abstract: This paper proposes a general approach to accounting for individual differences in the extreme response style in statistical models for ordered response categories. This approach uses a hierarchical ordinal regression modeling framework with heterogeneous thresholds structures to account for individual differences in the response style. Markov chain Monte Carlo algorithms for Bayesian inference for models with heterogeneous thresholds structures are discussed in detail. A simulation and two examples based on ordinal probit models are given to illustrate the proposed methodology. The simulation and examples also demonstrate that failing to account for individual differences in the extreme response style can have adverse consequences for statistical inferences.

Ordinal Analysis of Behavioral Data

Abstract: This chapter discusses statistical methods that make use of ordinal information. There are two main sections, the first covers ordinal measures of correlation and the second covers ordinal measures for group comparisons. The correlation section focuses on descriptive and inferential methods for the bivariate case. There is also a discussion of the comparison of ordinal correlations and a type of ordinal multiple regression. The group comparison section focuses on dominance analysis using the delta measure. Two-group and multiple-group situations are discussed as well as factorial designs and designs with correlated data. The methods of the chapter have many desirable properties that argue for their general use. Much data in the social sciences has only ordinal justification and ordinal methods are based on operations consistent with ordinal data. Many research questions in the social sciences are ordinal in nature and ordinal methods provide answers to ordinal questions. The ordinal methods have the advantage of invariance under monotonic transformations so that results obtained on raw data are exactly the same under any order-preserving transformation. Finally, the ordinal methods have desirable statistical qualities, including few distributional assumptions, resistance to extreme values, and applicability to nonlinear but monotonic relationships. Keywords: concordance; delta; distribution-free; dominance; nonparametric; ordinal; tau

Using the PLUM procedure of SPSS to fit unequal variance and generalized signal detection models.

Abstract: The recent addition of a procedure in SPSS for the analysis of ordinal regression models offers a simple means for researchers to fit the unequal variance normal signal detection model and other extended signal detection models. The present article shows how to implement the analysis and how to interpret the SPSS output. Examples of fitting the unequal variance normal model and other generalized signal detection models are given. The approach offers a convenient means for applying signal detection theory to a variety of research.

A practical SVM-based algorithm for ordinal regression in image retrieval

Abstract: Most current learning algorithms for image retrieval are based on dichotomy relevance judgement (relevant and non-relevant), though this measurement of relevance is too coarse. To better identify the user needs and preference, a good retrieval system should be able to handle multilevel relevance judgement. In this paper, we focus on relevance feedback with multilevel relevance judgment, where the relevance feedback is considered as an ordinal regression problem. Herbrich has proposed a support vector learning algorithm for ordinal regression based on the Linear Utility Model. His algorithm is intrinsically to train a SVM on a new derived training set, whose size increases rapidly when the original training set gets bigger. This property limits its applicability in relevance feedback, due to real-time requirement of the interactive process. By thoroughly analyzing Herbrich's algorithm, we first propose a new model for ordinal regression, called Cascade Linear Utility Model, then a practical SVM-based algorithm for image retrieval upon it. Our new algorithm is tested on a real-world image database, and compared with other three algorithms capable to handle multilevel relevance judgment. The experimental results show that the retrieval performance of our algorithm is comparable with that of Herbrich's algorithm but with only a fraction of its computational time, and apparently outperform the other methods.

Joint Regression and Association Modeling of Longitudinal Ordinal Data

Abstract: We propose models for longitudinal, or otherwise clustered, ordinal data. The association between subunit responses is characterized by dependence ratios (Ekholm, Smith, and McDonald, 1995, Biometrika 82, 847-854), which are extended from the binary to the multicategory case. The joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders, obtaining a computational advantage for likelihood-based inference. Equal emphasis is put on finding regression models for the univariate cumulative probabilities, and on deriving the dependence ratios from meaningful association-generating mechanisms. A data set on the effects of treatment with Fluvoxamine, which has been analyzed in parts before (Molenberghs, Kenward, and Lesaffre, 1997, Biometrika 84, 33-44), is analyzed in its entirety. Selection models are used for studying the sensitivity of the results to drop-out.

Comparison of two generalized logistic regression models; a case study

Abstract: Two generalized logistic regression models were compared on a set of observations describing persons with mental disabilities. The main variable of interest (willingness of the parents to incorporate their mentally handicapped offspring into on-farm activities) has three different values (no, undecided, yes). These values can be regarded as unordered (the variable having nominal measurement scale) or as ordered (the variable having ordinal measurement scale). Nominal and ordinal logistic regression models were used to analyze the impact of several predictors on the main variable of interest. We compare the two models in terms of the likelihood ratio test and the Nagelkerke coefficient of determination. It turns out that the ordinal regression assumptions are often not met. In our case, the nominal regression model has proved preferable to the ordinal regression one.

Three methods for analysing correlated ROC curves: a comparison in real data sets from multi-reader, multi-case studies with a factorial design

Abstract: This paper compares three published methods for analysing multiple correlated ROC curves: a method using generalized estimating equations with marginal non-proportional ordinal regression models; a method using jackknifed pseudovalues of summary statistics; a method using a corrected F-test from analysis of variance of summary statistics. Use of these methods is illustrated through six real data examples from studies with the common factorial design, that is, multiple readers interpreting images obtained with each test modality on each study subject. The issue of the difference between typical summary statistics and summary statistics from typical ROC curves is explored. The examples also address similarities and differences among the analytical methods. In particular, while point estimates of differences between test modalities are similar, the standard errors of these differences do not agree for all three methods. A simulation study supports the standard errors provided by the generalized estimating equations with marginal non-proportional ordinal regression models. Copyright ©2003 John Wiley & Sons, Ltd.

Multilevel relevance judgment, loss function, and performance measure in image retrieval

Abstract: Most learning algorithms for image retrieval are based on dichotomy relevance judgement (relevance and non-relevance), though this measurement of relevance is too coarse. To better identify the user needs and preference, a good retrieval system should be able to handle multilevel relevance judgement. In this paper, we focus on relevance feedback with multilevel relevance judgment. We consider relevance feedback as an ordinal regression problem, and discuss its properties and loss function. Since traditional performance measures such as precision and recall are based on dichotomy relevance judgment, we adopt a performance measure that is based on the preference of one image to another one. Furthermore, we develop a new relevance feedback scheme based on a support vector learning algorithm for ordinal regression. Our solution is tested on real image database, and promising results are achieved.

Ordinal regression modelling between proportional odds and non-proportional odds

Abstract: The proportional odds model has become the most widely used model in ordinal regression. Despite favourable properties in applications it is often an inappropriate simplification yielding bad data fit. The more flexible non-proportional odds model or partial proportional odds model have the disadvantage that common estimation procedures as Fisher scoring often fail to converge. Then neither estimates nor test statistics for the validity of partial proportional odds models are available. In the present paper estimates are proposed which are based on penalization of parameters across response categories. For appropriate smoothing penalized estimates exist almost always and are used to derive test statistics for the assumption of partial proportional odds. In addition, models are considered where the variation of parameters across response categories is constrained. Instead of using prespecified scalars (Peterson&Harrell 1990) penalized estimates are used in the identification of these constrained models. The methods are illustrated by various applications. The application to the retinopathy status in chronic diabetes shows how the proposed test statistics may be used in the diagnosis of partial proportional odds models in order to prevent artefacts.

Estimates, power and sample size calculations for two-sample ordinal outcomes under before-after study designs.

Abstract: Sample size calculations are given for comparing two groups of subjects, typically referring to active and non-active intervention groups, on an ordinal outcome in experiments where the subjects are measured before and after intervention. These calculations apply to log-odds models with random intercepts, treatment, time and treatment-by-time interaction terms, the latter being the term of interest. The assumed forms of the odds ratios are flexible, allowing for proportional odds, adjacent categories, or other conditional models for ordinal responses. Simulations studies show that, for given sample sizes, the nominal and actual powers of the proposed test are similar.

Monotonic decision tree for ordinal classification

Abstract: While ordinal classification problems are common in many situations, induction of ordinal decision trees has not been very extensiveness studied. They are commonly treated as nominal classification problem or regression problem in tree induction. On the other hand a monotonic decision tree is often desirable to aid decision making in such situations as credit rating and student admission. This paper proposes a novel approach called MDT to monotonic decision tree induction. Experiments show that generally this new approach produces decision trees that are more succinct and more effective predictors of the original implicit ordering, apart from being monotonic.

Incorporating Inter‐item Correlations in Item Response Data Analysis

Abstract: This paper concerns with the analysis of item response data, which are usually measured on a rating scale and are therefore ordinal. These study items tended to be highly inter-correlated. Rasch models, which convert ordinal categorical scales into linear measurements, are widely used in ordinal data analysis. In this paper, we improve the current methodology in order to incorporate inter-item correlations. We have advocated the latent variable approach for this purpose, in combination with generalized estimating equations to estimate the Rasch model parameters. The data on a study of families of lung cancer patients demonstrate the utility of our methods.

Ordinal Association Rules towards Association Rules

Abstract: Intensity of inclination, an objective rule-interest measure, allows us to extract implications on databases without having to go through the step of transforming the initial set of attributes into binary attributes, thereby avoiding obtaining a prohibitive number of rules of little significance with many redundancies. This new kind of rule, ordinal association rules, reveals the overall behavior of the population and it is vital that this study be extended by exploring specific ordinal association rules in order to refine our analysis and to extract behaviors in sub-sets. This paper focuses on the mining of association rules based on extracted ordinal association rules in order to, on the one hand remove the discretization step of numeric attributes and the step of complete disjunctive coding, and on the other hand obtain a variable discretization of numeric attributes i.e. dependent on association of attributes. The study ends with an evaluation of an application to some banking data.

Community Attachment and Quality of Life in Taiwan: An Application of Latent Class Analysis

Abstract: The concept of quality of life has been suggested to develop in regard to the mutual logical dependence between individual and society/community. Community, from the perspective of interactional theory, provides a setting and the mechanism of empirical contact between the individual and society. It is, therefore, essential to consider the role of community in terms of the sentiment and participation dimensions when studying individual life quality. This paper attempts to examine the contribution of community attachment to individual quality of life while controlling for sociodemographic characteristics. The data were drawn from the Taiwan Social Change Survey (Questionnaire No.2). A sample of 2,835 completed questionnaires was used for the analysis. Latent Class Analysis (LCA) was employed to reveal a latent structure of 32 participation patterns of community activities. A latent variable with four latent classes, namely fully involved participants, local activity participants, cultural activity participants, and unconcerned participants, was obtained as an indicator of the participation dimension of community attachment. Ordinal regression was employed to examine the effects of community attachment on individual quality of life. Both sentiment and participation dimensions of community attachment were found to contribute to a better quality of life. In addition, LCA was found to be a useful alternative to classification of community participation patterns. The results of this paper confirm the close association between community attachment and individual quality of life as well as provide a methodological contribution to sociology and community studies.

Novel Methods for Multivariate Ordinal Data Applied to Olympic Medals, Risk Profiles, Genomic Pathways, Genetic Haplotypes, Pattern Similarity, and Array Normalization

Abstract: In many applications, e.g., safety, security, biology, medicine, and pattern recognition, it is rare that a single variable is sufficient to represent all aspects of activity, risk, or response. Since complex systems tend to be neither linear, nor hierarchical in nature, but correlated and of unknown relative importance, the assumptions of traditional multivariate statistical methods can often not be justified on theoretical grounds. Establishing validity through empirical validation is not only problematic, but also time consuming. This paper proposes the use of u-statistics for scoring multivariate ordinal data and a family of simple non-parametric tests for analysis. The scoring method is demonstrated to be applicable to scoring profiles of Olympic medals, adverse events of different severity, and side effects of different category. It is then applied to identifying determinants (genomic pathways) that best correlated with complex responses to an intervention (treatment of psoriasis).

Ordinal association rules towards association rules

Abstract: Intensity of inclination, an objective rule-interest measure, allows us to extract implications on databases without having to go through the step of transforming the initial set of attributes into binary attributes, thereby avoiding obtaining a prohibitive number of rules of little significance with many redundancies. This new kind of rule, ordinal association rules, reveals the overall behavior of the population and it is vital that this study be extended by exploring specific ordinal association rules in order to refine our analysis and to extract behaviors in sub-sets. This paper focuses on the mining of association rules based on extracted ordinal association rules in order to, on the one hand remove the discretization step of numeric attributes and the step of complete disjunctive coding, and on the other hand obtain a variable discretization of numeric attributes i.e. dependent on association of attributes. The study ends with an evaluation of an application to some banking data.

A Model of Expert Investment Preferences on the Spanish Stock Exchange

Abstract: On the basis of data supplied by 36 questionnaire respondents, the investment preferences of professional investors on the Spanish stock exchange are modeled by ordinal and linear regression analyses in terms of the return, beta value, volatility and R2 of shares and the profits of the company. Ordinal regression was also used to obtain a model specific to the banking sector. The good fit of the models is interpreted as corroborating the rationality of professional investment decisions. In keeping with the experts' subjective assessments of the relative importance of the investment criteria, investment preferences were found to be based primarily on company profits.