Showing papers on "Ordinal regression published in 2011"
20 Jun 2011
TL;DR: The experimental results demonstrate that the proposed approach outperforms conventional multiclass-based and regression-based approaches as well as recently developed ranking-based age estimation approaches.
Abstract: In this paper, we propose an ordinal hyperplane ranking algorithm called OHRank, which estimates human ages via facial images. The design of the algorithm is based on the relative order information among the age labels in a database. Each ordinal hyperplane separates all the facial images into two groups according to the relative order, and a cost-sensitive property is exploited to find better hyperplanes based on the classification costs. Human ages are inferred by aggregating a set of preferences from the ordinal hyperplanes with their cost sensitivities. Our experimental results demonstrate that the proposed approach outperforms conventional multiclass-based and regression-based approaches as well as recently developed ranking-based age estimation approaches.
349 citations
01 Jan 2011
TL;DR: Christensen et al. as mentioned in this paper implemented cumulative link models in functions clm and clmm in package ordinal (clm, clmm) for ordinal data, which is a powerful model class for such data since observations are treated rightfully as categorical, the ordered nature is exploited and the flexible regression framework allows in-depth analyses.
Abstract: Ordered categorical data, or simply ordinal data, are commonplace in scientific disciplines where humans are used as measurement instruments. Examples include school gradings, ratings of preference in consumer studies, degree of tumor involvement in MR images and animal fitness in field ecology. Cumulative link models (Agresti, 2002) are a powerful model class for such data since observations are treated rightfully as categorical, the ordered nature is exploited and the flexible regression framework allows in-depth analyses. A pertinent latent variable interpretation of cumulative link models is an important aspect in many applications in sensometrics, psychometrics and other social sciences. Cumulative link (mixed) models are implemented in functions clm and clmm in package ordinal (Christensen, 2011).
143 citations
TL;DR: Whether and when fitting multilevel linear models to ordinal outcome data is justified and which estimator to employ when instead fitting multilesvel cumulative logit models to Ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL) is evaluated.
Abstract: Previous research has compared methods of estimation for multilevel models fit to binary data but there are reasons to believe that the results will not always generalize to the ordinal case. This paper thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, Maximum Likelihood (ML) or Penalized Quasi-Likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data includes a small to moderate number of clusters (i.e., ≤ 50 clusters).
116 citations
TL;DR: For a large data set there seems to be no explicit preference for either a frequentist or Bayesian approach (if based on vague priors), and on relatively large data sets, the different software implementations of logistic random effects regression models produced similar results.
Abstract: Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models. We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC. Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted. The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient. On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.
113 citations
TL;DR: In this paper, a new method, called ELECTREGKMS, which employs robust ordinal regression to construct a set of outranking models compatible with preference information, is presented, where preference information supplied by the decision maker is composed of pairwise comparisons stating the truth or falsity of the outranking relation for some real or fictitious reference alternatives.
104 citations
TL;DR: The goal of this work is to show that existing measures for evaluating ordinal classification models suffer from a number of important shortcomings, and to propose an alternative measure defined directly in the confusion matrix, which confirms the usefulness of the novel metric.
Abstract: Ordinal classification is a form of multiclass classification for which there is an inherent order between the classes, but not a meaningful numeric difference between them. The performance of such classifiers is usually assessed by measures appropriate for nominal classes or for regression. Unfortunately, these do not account for the true dimension of the error. The goal of this work is to show that existing measures for evaluating ordinal classification models suffer from a number of important shortcomings. For this reason, we propose an alternative measure defined directly in the confusion matrix. An error coefficient appropriate for ordinal data should capture how much the result diverges from the ideal prediction and how "inconsistent" the classifier is in regard to the relative order of the classes. The proposed coefficient results from the observation that the performance yielded by the Misclassification Error Rate coefficient is the benefit of the path along the diagonal of the confusion matrix. We carry out an experimental study which confirms the usefulness of the novel metric.
95 citations
TL;DR: A way of selecting a representative value function among the set of compatible ones so that the selected function highlights the most stable part of the robust sorting, and can be perceived as representative in the sense of robustness preoccupation.
85 citations
TL;DR: Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure, and the roleof data structure is investigated.
51 citations
TL;DR: In this article, the ordinal structure is taken into account by use of a difference penalty on adjacent dummy coefficients, and an alternative blockwise boosting procedure is proposed to select ordinally scaled independent variables in the classical linear model.
Abstract: Summary. Ordinal categorial variables arise commonly in regression modelling. Although the analysis of ordinal response variables has been well investigated, less work has been done concerning ordinal predictors. We consider so-called international classfication of functioning core sets for chronic widespread pain, in which many ordinal covariates are collected. The effect of specific international classification of functioning variables on a subjective measure of physical health is investigated, which requires strategies for variable selection. In this context, we propose methods for the selection of ordinally scaled independent variables in the classical linear model. The ordinal structure is taken into account by use of a difference penalty on adjacent dummy coefficients. It is shown how the group lasso can be used for the selection of ordinal predictors, and an alternative blockwise boosting procedure is proposed. Both methods are discussed in general, and applied to international classification of functioning core sets for chronic widespread pain.
38 citations
TL;DR: In this paper, a Bayesian shrinkage estimator is proposed to model ordinal treatment variables, which allows the model to contain both individual group level indicators and a continuous predictor.
Abstract: Ordinal variables—categorical variables with a defined order to the categories, but without equal spacing between them—are frequently used in social science applications. Although a good deal of research exists on the proper modeling of ordinal response variables, there is not a clear directive as to how to model ordinal treatment variables. The usual approaches found in the literature for using ordinal treatment variables are either to use fully unconstrained, though additive, ordinal group indicators or to use a numeric predictor constrained to be continuous. Generalized additive models are a useful exception to these assumptions (Beck and Jackman 1998). In contrast to the generalized additive modeling approach, we propose the use of a Bayesian shrinkage estimator to model ordinal treatment variables. The estimator we discuss in this paper allows the model to contain both individual group level indicators and a continuous predictor. In contrast to traditionally used shrinkage models that pull the data toward a common mean, we use a linear model as the basis. Thus, each individual effect can be arbitrary, but the model “shrinks” the estimates toward a linear ordinal framework according to the data. We demonstrate the estimator on two political science examples: the impact of voter identification requirements on turnout (Alvarez, Bailey, and Katz 2007), and the impact of the frequency of religious service attendance on the liberality of abortion attitudes (e.g., Singh and Leahy 1978, Tedrow and Mahoney 1979, Combs and Welch 1982).
37 citations
TL;DR: The notion of a Lipschitz smoothness constant is found to be useful for complexity control for learning transformation models, much in a similar vein as the 'margin' is for Support Vector Machines for classification.
Abstract: This paper studies the task of learning transformation models for ranking problems, ordinal regression and survival analysis The present contribution describes a machine learning approach termed MINLIP The key insight is to relate ranking criteria as the Area Under the Curve to monotone transformation functions Consequently, the notion of a Lipschitz smoothness constant is found to be useful for complexity control for learning transformation models, much in a similar vein as the 'margin' is for Support Vector Machines for classification The use of this model structure in the context of high dimensional data, as well as for estimating non-linear, and additive models based on primal-dual kernel machines, and for sparse models is indicated Given n observations, the present method solves a quadratic program existing of O(n) constraints and O(n) unknowns, where most existing risk minimization approaches to ranking problems typically result in algorithms with O(n2) constraints or unknowns We specify the MINLIP method for three different cases: the first one concerns the preference learning problem Secondly it is specified how to adapt the method to ordinal regression with a finite set of ordered outcomes Finally, it is shown how the method can be used in the context of survival analysis where one models failure times, typically subject to censoring The current approach is found to be particularly useful in this context as it can handle, in contrast with the standard statistical model for analyzing survival data, all types of censoring in a straightforward way, and because of the explicit relation with the Proportional Hazard and Accelerated Failure Time models The advantage of the current method is illustrated on different benchmark data sets, as well as for estimating a model for cancer survival based on different micro-array and clinical data sets
TL;DR: Through exploiting the separability of the Hessian, this work provides a unified approach, from an optimization perspective, to 1- norm classification, 2-norm classification, universum classification, ordinal regression and ε-insensitive regression.
Abstract: Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only $\mathcal{O}(n)$ operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm classification, universum classification, ordinal regression and ?-insensitive regression. Our approach has the added advantage of obtaining the hyperplane weights and bias directly from the solver. Numerical experiments indicate that, in contrast to existing methods, the algorithm is largely unaffected by noisy data, and they show training times for our implementation are consistent and highly competitive. We discuss the effect of using multiple correctors, and monitoring the angle of the normal to the hyperplane to determine termination.
TL;DR: Under the proposed framework of kernelized OPP (KOPP), the nonlinear relationship and, more importantly, efficiently fuse acoustic and symbolic features obtained from the artist recommended meta-data are derived.
Abstract: This paper proposes a content-based artist recommendation framework which learns relationships between users' preference and music contents through ordinal regression. In particular, an artist is characterized by the parameters of its corresponding acoustical model which is adapted from a universal background model. These artist-specific acoustic features together with their preference rankings are then used as input vectors for the proposed order preserving projection (OPP) algorithm which tries to find a suitable subspace such that the desired ranking order of the data after projection can be kept as much as possible. The proposed linear OPP can be kernelized to learn the nonlinear relationship between music contents and users' artist rank orders. Under the proposed framework of kernelized OPP (KOPP), we can derive the nonlinear relationship and, more importantly, efficiently fuse acoustic and symbolic features obtained from the artist recommended meta-data. Experimental results demonstrate that OPP attains comparable results with those obtained with a conventional ordinal regression method, Prank. Moreover, by exploring the nonlinear relationship among training examples and combining acoustic and symbolic features, KOPP outperforms previous approaches to artist recommendation.
28 Nov 2011
TL;DR: This paper presents a novel algorithm called manifold ordinal regression (MOR) for image ranking, capable of uncovering the intrinsically nonlinear structure held by the image data sets, and provides faithful rating to the new coming images.
Abstract: In this paper, we present a novel algorithm called manifold ordinal regression (MOR) for image ranking. By modeling the manifold information in the objective function, MOR is capable of uncovering the intrinsically nonlinear structure held by the image data sets. By optimizing the ranking information of the training data sets, the proposed algorithm provides faithful rating to the new coming images. To offer more general solution for the real-word tasks, we further provide the semi-supervised manifold ordinal regression (SS-MOR). Experiments on various data sets validate the effectiveness of the proposed algorithms.
01 Nov 2011
TL;DR: A pair of metrics are selected to guide the evolution of a multi-objective evolutionary algorithm, obtaining good results in generalization on ordinal datasets.
Abstract: There are many metrics available to measure the goodness of a classifier when working with ordinal datasets. These measures are divided into product-moment and association metrics. In this paper, the behavior of several metrics is studied in different situations. In addition, two new measures associated with an ordinal classifier are defined: the maximum and the minimum mean absolute error of all the classes. From the results of this comparison, a pair of metrics is selected (one associated to the overall error and another one to the error of the class with lowest level of classification) to guide the evolution of a multi-objective evolutionary algorithm, obtaining good results in generalization on ordinal datasets.
TL;DR: The theoretical features and properties, which include parameters, variable selection, and model evaluation, followed by comparisons of the disadvantages and advantages of both models were analytically reviewed.
Abstract: Many social studies analyze attitude responses using the linear regression model. This model typically treats questionnaire data as continuous scales, although the data is merely ordinal. One type of regression model that is more appropriate to analyze rank-order responses is the Ordinal Logistic Regression (OLR) model. In addition to the use of regression, the Artificial Neural Network (ANN) model has recently been applied in various studies. This paper delivered comparative descriptions of both the ANN and OLR models. The theoretical features and properties, which include parameters, variable selection, and model evaluation, followed by comparisons of the disadvantages and advantages of both models were analytically reviewed. [Service Science, ISSN 2164-3962 (print), ISSN 2164-3970 (online), was published by Services Science Global (SSG) from 2009 to 2011 as issues under ISBN 978-1-4276-2090-3.]
Proceedings Article•
07 Aug 2011TL;DR: This paper presents a novel ordinal regression approach via manifold learning, which is capable of uncovering the embedded nonlinear structure of the data set according to the observations in the high-dimensional feature space by optimizing the order information of the observations and preserving the intrinsic geometry of theData set simultaneously.
Abstract: Ordinal regression is an important research topic in machine learning. It aims to automatically determine the implied rating of a data item on a fixed, discrete rating scale. In this paper, we present a novel ordinal regression approach via manifold learning, which is capable of uncovering the embedded nonlinear structure of the data set according to the observations in the high-dimensional feature space. By optimizing the order information of the observations and preserving the intrinsic geometry of the data set simultaneously, the proposed algorithm provides the faithful ordinal regression to the new coming data points. To offer more general solution to the data with natural tensor structure, we further introduce the multilinear extension of the proposed algorithm, which can support the ordinal regression of high order data like images. Experiments on various data sets validate the effectiveness of the proposed algorithm as well as its extension.
22 May 2011
TL;DR: A method to automatically quantify the approach-and-avoidance (AA) behavior, described by ordinal labels manually assigned by experts using either video-only or video-with-audio, is described.
Abstract: Behavioral Signal Processing aims at automating behavioral coding schemes such as those prevalent in psychology and mental health research. This paper describes a method to automatically quantify the approach-and-avoidance (AA) behavior, described by ordinal labels manually assigned by experts using either video-only or video-with-audio. We propose a novel ordinal regression (OR) algorithm and its hidden Markov model (HMM) extension for estimation of AA labels from visual motion capture based and acoustic features. The proposed algorithm transforms the OR to multiple binary classification problems, solves them by independent score-outputting classifiers and fits the cumulative logit logistic regression model with proportional odds (CLLRMP) to vectors of the classifier scores. The time series extension treats labels as states of the HMM with a likelihood function derived from the probabilistic CLLRMP output. We compare performances of the proposed algorithm applying the weighted binary SVMs in the second step (SVM-OLR), its time-series extension (HMM-SVM-OLR) and the baseline multi-class SVM. On the used dyadic interaction dataset the HMM-SVM-OLR achieves the highest estimation accuracies 71.6 % and 65.7 % for AA labels assigned respectively using video-only and video-with-audio.
24 Oct 2011
TL;DR: This paper presents a study of machine learning approaches to email prioritization into discrete levels, comparing ordinal regression versus classifier cascades, and finds a cascade of SVM classifiers significantly outperforms Ordinal regression forEmail prioritization.
Abstract: Email overload, even after spam filtering, presents a serious productivity challenge for busy professionals and executives. One solution is automated prioritization of incoming emails to ensure the most important are read and processed quickly, while others are processed later as/if time permits in declining priority levels. This paper presents a study of machine learning approaches to email prioritization into discrete levels, comparing ordinal regression versus classifier cascades. Given the ordinal nature of discrete email priority levels, SVM ordinal regression would be expected to perform well, but surprisingly a cascade of SVM classifiers significantly outperforms ordinal regression for email prioritization. In contrast, SVM regression performs well -- better than classifiers -- on selected UCI data sets. This unexpected performance inversion is analyzed and results are presented, providing core functionality for email prioritization systems.
TL;DR: The aim of this article is to introduce a new clustering method suitably planned for ordinal data that allows to overcome two typical problems of cluster analysis: the choice of the number of groups and the scale invariance.
Abstract: Often, categorical ordinal data are clustered using a well-defined similarity measure for this kind of data and then using a clustering algorithm not specifically developed for them. The aim of this article is to introduce a new clustering method suitably planned for ordinal data. Objects are grouped using a multinomial model, a cluster tree and a pruning strategy. Two types of pruning are analyzed through simulations. The proposed method allows to overcome two typical problems of cluster analysis: the choice of the number of groups and the scale invariance.
Posted Content•
TL;DR: In this paper, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function and the loss in efficiency due to the weighting is limited.
Abstract: Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.
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TL;DR: oglm as discussed by the authors is a tool for estimating OLSM models that explicitly specify the determinants of heteroskedasticity in an attempt to understand and correct for errors in OLS regression.
Abstract: oglm estimates Ordinal Generalized Linear Models. It supports several link functions, including logit, probit, complementary log-log, log-log and cauchit. When an ordinal regression model incorrectly assumes that error variances are the same for all cases, the standard errors are wrong and (unlike OLS regression) the parameter estimates are biased. With oglm you can estimate heterogeneous choice/ location-scale models that explicitly specify the determinants of heteroskedasticity in an attempt to understand and correct for it. Several other special cases of ordinal generalized linear models can also be estimated by oglm. oglm was inspired by the SPSS PLUM routine but differs somewhat in its terminology, labeling of links, and the variables that are allowed when modeling heteroskedasticity. oglm9 is the last version of oglm that runs on Stata 9 & 10. Stata 11+ users should use oglm instead.
TL;DR: The first rigorous analysis of national food security levels in post conflict South Sudan is presented and the power of the Ordinal Logistic Regression model is shown in identifying significant predictors of food insecurity, surveillance, monitoring and early warning.
Abstract: The lack of a “gold standard” to determine and predict household food insecurity is well documented. While a considerable volume of research continues to explore universally applicable measurement approaches, robust statistical techniques have not been applied in food security monitoring and early warning systems, especially in countries where food insecurity is chronic. This study explored the application of various Ordinal Logistic Regression techniques in the analysis of national data from South Sudan. Five Link Functions of the Ordinal Regression model were tested. Of these techniques, the Probit Model was found to be the most efficient for predicting food security using ordered categorical outcomes (Food Consumption Scores). The study presents the first rigorous analysis of national food security levels in post conflict South Sudan and shows the power of the model in identifying significant predictors of food insecurity, surveillance, monitoring and early warning.
09 Nov 2011
TL;DR: In this paper, the authors tackle the topics of robustness and multivariate outlier detection for ordinal data and illustrate how to detect atypical measurements in customer satisfaction surveys.
Abstract: This chapter tackles the topics of robustness and multivariate outlier detection for ordinal data. We initially review outlier detection methods in regression for continuous data and give an example which shows that graphical tools of data analysis or traditional diagnostic measures based on all the observations are not sufficient to detect multivariate atypical observations. Then we focus on ordinal data and illustrate how to detect atypical measurements in customer satisfaction surveys. Next, we review the generalized linear model of ordinal regression and apply it to the ABC survey. The chapter concludes with an analysis of a set of diagnostics to check the goodness of the suggested model and the presence of anomalous observations.
TL;DR: This paper describes a macro program on how to generate correlated ordinal data based on R language and SAS IML and provides a tool for generating correlated ordinals data to be used in simulation studies.
TL;DR: In this paper, the authors investigated recent trends in tourism firms' location decisions in Greece in relation to the state policy on tourism investment incentives as well as specific factors concerning regional inherent and created resources.
Abstract: This article investigates recent trends in tourism firms' location decisions in Greece in relation to the state policy on tourism investment incentives as well as specific factors concerning regional inherent and created resources. By means of an ordinal regression analysis, we set up a spatial model of private investments in tourism accommodation at the prefectural level (NUTS III) for the period from 1991 to 1998. The actual influence of the individual factors varies considerably. Prefectures with limited natural coastal resources, inadequate transportation infrastructure and low expertise may be less capable of attracting new tourism investments. However, their inability is partly due to the general focus of the country to mass recreational tourism. Planning and applying a more effective regional tourism policy should involve specifying the objectives of the tourism sector as well as identifying the critical regional factors that are favourable and unfavourable towards achieving those objectives.
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TL;DR: oglm as discussed by the authors is a tool for estimating OLSM models that explicitly specify the determinants of heteroskedasticity in an attempt to understand and correct for errors in OLS regression.
Abstract: oglm estimates Ordinal Generalized Linear Models. It supports several link functions, including logit, probit, complementary log-log, log-log and cauchit. When an ordinal regression model incorrectly assumes that error variances are the same for all cases, the standard errors are wrong and (unlike OLS regression) the parameter estimates are biased. With oglm you can estimate heterogeneous choice/ location-scale models that explicitly specify the determinants of heteroskedasticity in an attempt to understand and correct for it. Several other special cases of ordinal generalized linear models can also be estimated by oglm. oglm was inspired by the SPSS PLUM routine but differs somewhat in its terminology, labeling of links, and the variables that are allowed when modeling heteroskedasticity. oglm9 is the last version of oglm that runs on Stata 9 & 10. Stata 11+ users should use oglm instead.
TL;DR: In this paper, an alternative (restricted) likelihood ratio test for ordinal predictors with ordered levels is proposed, which is based on the mixed model formulation of penalized dummy coefficients.
Abstract: In a linear model relevance of a categorical predictor with ordered levels is typically tested by use of the standard F-test (known from statistical textbooks). Such a test can also be applied for testing whether the regression function is linear in the ordinal predictor’s class labels. In this paper we propose an alternative (restricted) likelihood ratio test for these hypotheses which is especially suited for ordinal predictors and is based on the mixed model formulation of penalized dummy coefficients. We show in simulation studies that the new test is more powerful than the standard F-test in many situations. The advantage of the new test is especially striking when the number of ordered levels is moderate or large. Using the relationship to mixed effect models and robust existent fitting software obtaining the test and its null distribution is very fast; a fast R implementation is provided.
TL;DR: In this article, a flexible skewed link function for modeling ordinal response data with covariates based on the generalized extreme value (GEV) distribution is introduced, which automatically detects the skewness in the response curve along with the model fitting.
Abstract: This paper introduces a flexible skewed link function for modeling ordinal response data with covariates based on the generalized extreme value (GEV) distribution. Commonly used probit, logit and complementary log-log links are prone to link misspecification because of their fixed skewness. The GEV link is flexible in fitting the skewness in the response curve with a free shape parameter. Using Bayesian methodology, it automatically detects the skewness in the response curve along with the model fitting. The flexibility of the proposed model is illustrated by its application to an ecological survey data about the coverage of Berberis thunbergii in New England. We employ the latent variable approach by Albert and Chib (J Am Stat Assoc 88:669–679, (1993) to develop computational schemes. For model selection, we employ the Deviance Information Criterion (DIC).