assessing proportionality in the proportional odds model for ordinal logistic regression the proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories the model may be represented by a series of logistic regressions for dependent binary variables with common regression parameters reflecting the proportional odds assumption key to the valid application of the model is the assessment of the proportionality assumption an approach is described arising from comparisons of the separate correlated fits to the binary logistic models underlying the overall model based on asymptotic distributional results formal goodness of fit measures are constructed to supplement informal comparisons of the different fits a number of proposals including application of bootstrap simulation are discussed and illustrated with a data example

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

discrimination and classification overview publisher summary this chapter discusses discrimination and classification the problem of discrimination and classification is mainly concerned with differentiating between g g 2 mutually exclusive populations and with classifying subjects or objects on the basis of multivariate observation the emphasis of the problem is on deriving a rule that can be used to optimally classify a new subject it is an important problem in statistics and applied mathematics as its applications are found in many diverse areas in practice the distributions are rarely known and if the form of the distributions are known or assumed the parameters are seldom known thus the problem for practical applications is to develop a sample based rule for discrimination and classification the earliest and most well known method is based on the linear discriminant function due to fisher

malliavin calculus in abstract wiener space using infinitesimals abstract using infinitesimals we develop malliavin calculus on spaces which result from the classical wiener space c 0 1 r by replacing r with any abstract wiener space h b we start from a brownian motion b on a loeb probability space with values in the banach space b b is the standard part of a finite dimensional brownian motion b then we define iterated ito integrals as standard parts of internal iterated ito integrals the integrator of the internal integrals is b and the values of the integrands are multilinear forms on f n where f is a finite dimensional linear space over r between the hilbert space h and its extension h in the first part we prove a chaos decomposition theorem for l2 functionals on that are measurable with respect to the algebra generated by b this result yields a chaos decomposition of l2 functionals with respect to the wiener measure on the standard space c b of b valued continuous functions on 0 1 in the second part we define the malliavin derivative and the skorohod integral as standard parts of internal operators defined on finite dimensional spaces in an application we use the transformation rule for finite dimensional euclidean spaces to study time anticipating and non anticipating shifts of brownian motion by bochner integrals girsanov transformations

hypothesis testing in the polychotomous logistic model with an application to detecting gastrointestinal cancer we discuss the use of the trichotomous logistic model to discriminate between patients with gastrointestinal gi cancer patients with benign gi disease and normal subjects using symptoms and the concentrations of some serum proteins that are potentially indicative of malignancy as covariates a parsimonious model can be obtained by invoking an indistinguishability hypothesis which is appropriate when a covariate is considered to have no predictive value between categories it is shown that the polychotomous model can be re parameterised under the null hypothesis to give a reduced form which can be fitted by maximum likelihood the validity of the use of the same methods for retrospective sampling is discussed the approach is illustrated by the development of a logistic model to identify symptomatic and asymptomatic subjects with a high risk of gi cancer

a two stage regression model for epidemiological studies with multivariate disease classification data polytomous logistic regression is commonly used to analyze epidemiological data with disease subtype information in this approach effects of exposures on different disease subtypes are studied through separate exposure odds ratios comparing different case groups to the common control group this article considers the situation where disease subtypes can be defined using multiple characteristics of a disease for efficient analysis of such data a two stage modeling approach is proposed at the first stage a standard polytomous logistic regression model is considered for all possible distinct disease subtypes that can be defined by the cross classification of the different disease characteristics at the second stage the exposure odds ratio parameters for the first stage disease subtypes are further modeled in terms of the defining characteristics of the subtypes when the total number of first stage disease subtypes is small standard maximum likelihood methods can be used for inference in the proposed

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

retrospective prospective symmetry in the likelihood and bayesian analysis of case control studies summary prentice pyke 1979 established that the maximum likelihood estimate of an odds ratio in a case control study is the same as would be found by fitting a logistic regression in other words for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model similar results have been obtained for other models and conditions have also been identified under which the corresponding bayesian property holds namely that the posterior distribution of the odds ratio is the same whether it is computed using the prospective or the retrospective likelihood in this article we demonstrate how these results follow directly from certain parameter independence properties of the models and priors and identify prior laws that support such reverse analysis for both standard and stratified designs somekeywords case controlstudy conditionalindependence hypermarkovlaw logisticregression retrospective likelihood

generalized estimating equations to estimate the ordered stereotype logit model for panel data by modeling the effects of predictor variables as a multiplicative function of regression parameters being invariant over categories and category specific scalar effects the ordered stereotype logit model is a flexible regression model for ordinal response variables in this article we propose a generalized estimating equations gee approach to estimate the ordered stereotype logit model for panel data based on working covariance matrices which are not required to be correctly specified a simulation study compares the performance of gee estimators based on various working correlation matrices and working covariance matrices using local odds ratios estimation of the model is illustrated using a real world dataset the results from the simulation study suggest that gee estimation of this model is feasible in medium sized and large samples and that estimators based on local odds ratios as realized in this study tend to be less efficient compared with estimators based on a working correlation matrix for low true correlations the efficiency gains seem to be rather small and if the working covariance structure is too flexible the corresponding estimator may even be less efficient compared with the gee estimator assuming independence like for gee estimators more generally if the true correlations over time are high then a working covariance structure which is close to the true structure can lead to considerable efficiency gains compared with assuming independence

k duality for pseudomanifolds with isolated singularities abstract we associate to a pseudomanifold x with a conical singularity a differentiable groupoid g which plays the role of the tangent space of x we construct a dirac element and a dual dirac element which induce a k duality between the c algebras c g and c x this is a first step toward an index theory for pseudomanifolds

a goodness of fit test for the ordered stereotype model this paper presents a new goodness of fit test for an ordered stereotype model used for an ordinal response variable the proposed test is based on the well known hosmer lemeshow test and its version for the proportional odds regression model the latter test statistic is calculated from a grouping scheme assuming that the levels of the ordinal response are equally spaced which might be not true one of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories dictated by the data the proposed test takes the use of this new adjusted spacing to partition data a simulation study shows good performance of the proposed test under a variety of scenarios finally the results of the application in two examples are presented copyright 2016 john wiley sons ltd

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

the grouped continuous model for multivariate ordered categorical variables and covariate adjustment the grouped continuous model for multivariate ordered categorical data is described this is based on partitioning an underlying multivariate normal distribution straightforward maximum likelihood estimation is really feasible only for one and two way tables we introduce an estimation system based on maximum likelihood estimation in the one and two way marginal tables of higher order tables this is computationally feasible and an example involving aspects of bird colouring is given the approach is extended to provide a regression model for multivariate ordered categorical data with an estimation scheme again based on the one and two way marginal tables the above example is developed to investigate the covariate effect of time the asymptotic efficiency of these sampling schemes is discussed it appears that they have high efficiency

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

computing exact distributions for polytomous response data abstract this article presents an efficient method for computing exact conditional distributions of the sufficient statistics for the parameters of four polytomous response models for nominal response two baseline category logit models and for ordinal response two adjacent categories logit models are considered the method consists of recursive generation of the joint distribution of the sufficient statistics augmented by a technique to slice off portions of the evolving sample space so as to eventually yield the required conditional distribution two actual data sets are analyzed to illustrate the method

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

a class of logistic regression models for multivariate binary time series abstract a logistic model for multivariate binary time series is proposed first we establish the equivalence between a log linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others the logistic formulation is used to describe a markov chain for each series which implies a markov model for the vector of time series a pseudolikelihood estimation procedure is presented the methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health maintenance plan

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

independent random partial matching with general types abstract we provide a mathematical foundation for an independent random partial matching with a continuum of agents where the type space is not necessarily finite besides establishing the existence result we also identify the deterministic distributions of matched types in the matching our results are based on the fubini property for loeb product spaces and products of loeb transition probabilities as well as keisler s homogeneity theorem for loeb counting probability spaces

missing exposure data in stereotype regression model application to matched case control study with disease subclassification with advances in modern medicine and clinical diagnosis case control data with characterization of finer subtypes of cases are often available in matched case control studies missingness in exposure values often leads to deletion of entire stratum and thus entails a significant loss in information when subtypes of cases are treated as categorical outcomes the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category specific odds ratio parameters especially using the multinomial logit model the stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model the use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters we illustrate how to handle missing data in matched case control studies with finer disease subclassification within the cases under a stereotype regression model we present both monte carlo based full bayesian approach and expectation conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism we illustrate our methods by using data from an ongoing matched case control study of colorectal cancer simulation results are presented under various missing data mechanisms and departures from modeling assumptions

bayesian inference for the stereotype regression model application to a case control study of prostate cancer the stereotype regression model for categorical outcomes proposed by anderson j roy statist soc b 1984 46 1 30 is nested between the baseline category logits and adjacent category logits model with proportional odds structure the stereotype model is more parsimonious than the ordinary baseline category or multinomial logistic model due to a product representation of the log odds ratios in terms of a common parameter corresponding to each predictor and category specific scores the model could be used for both ordered and unordered outcomes for ordered outcomes the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable but are inherently multi dimensional in nature as pointed out by greenland statist med 1994 13 1665 1677 an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome stratified sampling as in case control studies in addition for matched case control studies the stereotype model is amenable to classical conditional likelihood principle whereas there is no reduction due to sufficiency under the proportional odds model in spite of these attractive features the model has been applied less as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non linearity and lack of identifiability of the parameters we present comprehensive bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach we illustrate our methodology by analyzing data from the flint men s health study a case control study of prostate cancer in african american men aged 40 79 years we use clinical staging of prostate cancer in terms of tumors nodes and metastasis as the categorical response of interest

uncorrelatedness and orthogonality for vector valued processes for a square integrable vector valued process f on the loeb product space it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality various characterizations of almost sure uncorrelatedness for f are presented the process f is also related to multilinear forms on the target hilbert space finally a general structure result for f involving the biorthogonal representation for the conditional expectation of f with respect to the usual product algebra is presented

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

some remarks on kasparov theory on considere une autre preuve de l invariance d homotopie du bifoncteur ext on etudie l associativite du produit de kasparov a travers la motion de connextion

constrained latent class analysis simultaneous classification and scaling of discrete choice data a reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data latent class specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal point or vector model that yields a graphical multidimensional representation of the classification results in addition background variables can be incorporated as an aid to interpreting the latent class specific response probabilities the analyses of synthetic and real data sets illustrate the proposed method

analysis of ordinal data in a study of endometrial cancer under a matched pairs case control design while estimating odds ratios ors in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer the categories formed by the levels of the exposure are ordinal in nature in the literature the binary logistic model is used for estimating or for each category relative to the baseline category we describe the use of two ordinal logistic models the cumulative logit and continuation ratio logit models to estimate the ors for the matched pairs case control data set of the los angeles endometrial cancer study a test for equality of the cumulative ors across the exposure levels is proposed the test statistic follows asymptotically the chi square distribution

k theoretic amenability for sl2 qp and the action on the associated tree abstract it is proved that if a locally compact group g acts simplicially on a tree in such a way that the stabilizers of the vertices are amenable then g is k amenable in particular the canonical map from the full c algebra onto the reduced c algebra of g induces isomorphisms in k theory the main corollary of our result is that sl 2 q p and some other groups over local fields are k amenable

bootstrap choice of estimators in parametric and semiparametric families an extension of eic ishiguro sakamoto et kitagawa 1997 ont propose le eic comme une extension du critere d akaike aic le eic est construit en corrigeant le biais de la log vraisemblance consideree comme un estimateur de l information de kullback leibler par la technique du bootstrap nous developpons ce critere dans un cadre d estimation semi parametrique multivarie et nous montrons qu il peut etre utilise pour choisir un estimateur parmi une famille d estimateurs parametriques et semi parametriques une etude de simulation basee sur un modele de regression montre que l eic est meilleur que les criteres usuels bien que la validation croisee appliquee a la vraisemblance donne des resulats tres proches sauf dans le cas d echantillons de faible taille nous avons applique le eic afin d estimer l evolution moyenne de la charge virale d enfants infectes par le vih

unimodal models to relate species to environment to assess the impact of environmental change on biological communities knowledge about species environment relationships is indispensable ecologists attempt to uncover the relationships between species and environment from data obtained from field surveys in the survey species are scored on their presence or their abundance at each of several sampling sites and environmental variables that ecologists believe to be important are measured the research that led to this thesis aimed to unravel the assumptions required for the application of statistical methods that are popular among ecologists to analyse such data from a statistical point of view species data are difficult to analyse there are many species involved 10 500 many species occur at a few sites only so the data contain numerous zeroes relations between species and environmental variables are not linear but unimodal a plant for example preferably grows under for that species optimal moisture conditions and is encountered less frequently at drier or wetter sites a mathematical model for a unimodal relationship is the gaussian response model standard statistical methods such as linear regression principal components analysis and canonical correlation analysis are often inappropriate for analysing species data because they are based on linear relationships one of the methods that ecologists use instead is correspondence analysis this thesis contributes to the understanding of the underlying response model with correspondence analysis species and sites are arranged to discover the structure in the data ordination and the arrangement is subsequently related to environmental variables it is an indirect method to detect relations between species and environment hence r h whittaker s term indirect gradient analysis correspondence analysis has been invented around 1935 but did not receive interest from ecologists before 1973 when m o hill derived the technique once more as the repeated application of weighted averaging a method that was familiar to ecologists ever since 1930 weighted averaging has the advantage of being simple to apply the method can be used for two different aims 1 to estimate the optimum of a species for an environmental variable and 2 to estimate the value of an environmental variable at a site from known optima of the species present calibration in chapter 2 estimating optima by weighted averaging is compared with the results of non linear regression on the basis of the gaussian response model under particular conditions both methods agree precisely in other cases weighted averaging gives a biased estimate of the optimum and non linear regression is the method to be preferred an additional advantage of non linear regression is that it can also be used to fit response models with more than one environmental variable in chapter 3 weighted averaging to estimate the value of an environmental variable is compared with calibration on the basis of the gaussian response model also in this context the techniques are sometimes equivalent chapter 4 deals with correspondence analysis it is shown that under particular conditions correspondence analysis approximates ordination on the basis of the gaussian response model which is computationally much more complicated to detect relations indirect methods have an important disadvantage the impact of some environmental variables on the species composition can be so large that the impact of other interesting environmental variables may fail to be detected this problem can be overcome by using non linear regression but with many species and environmental variables this is laborious in chapter 5 a simpler direct method is proposed canonical correspondence analysis in chapter 6 canonical correspondence analysis turns out to be a multivariate extension of weighted averaging the results can be displayed graphically in chapter 7 an extension with covariables is discussed which leads to partial canonical correspondence analysis chapter 7 also shows that gaussian models and hence canonical correspondence analysis are relevant to the analysis of contingency tables chapter 8 describes a study to estimate ecological amplitudes of plant species with respect to ellenberg s moisture scale from species data alone the question that is addressed as well is how consequent ellenberg s moisture indicator values are finally chapter 9 cross tabulates various gradient analysis techniques by the type of problem regression calibration ordination etc and the response model linear or unimodal furthermore improvements are proposed for detrended correspondence analysis a computer program named mom is written which can perform most of the methods discussed

standardized estimates from categorical regression models we consider the problem of interpreting categorical regression models such as the polytomous logistic model the continuation ratio model the stereotype model and the cumulative odds model we present a method to convert categorical regression coefficients into estimates of standardized fitted probabilities probability differences and probability ratios we use a delta method approach to estimate standard errors we then present a small simulation study to compare different transforms for setting confidence limits and provide an illustration of our approach in an observational study of drug therapy of polymyositis

holonomy groupoids of singular foliations we give a new construction of lie groupoids which is particularly well adapted to the generalization of holonomy groupoids to singular foliations given a family of local lie groupoids on open sets of a smooth manifold m satisfying some hypothesis we construct a lie groupoid which contains the whole family this construction involves a new way of considering local morita equivalences not only as equivalence relations but also as generalized isomorphisms in particular we prove that almost injective lie algebroids are integrable

a note on regression analysis of ordinal data with variability of classification summary the effect of observation variability in the classification of an ordinal response is examined within the framework of the proportional hazards regression model for ordinal data a model is proposed which incorporates this type of variability and the behaviour of the proportional hazards model when this new model is appropriate is examined four data sets are used to illustrate the practical application of the model

classification efficiency of multinomial logistic regression relative to ordinal logistic regression abstract classification procedures are useful for the prediction of a response or outcome as a result of knowledge of the levels of one or more independent or predictor variables the procedure is said to classify the possibly multivariate observation to a level of the response variable an example might be the prediction of whether an individual will be well suffer a nonfatal heart attack or suffer a fatal heart attack this prediction might be made on the basis of the levels of various independent variables such as weight blood pressure and serum cholesterol to name a few the three response categories of the aforementioned example are ordinal an example of three nonordered response categories might be as follows well death from heart attack and death from cancer there is some recent interest in ordinal classification procedures it is reasonable to assume that when the response variable is ordinal inclusion of ordinality in the classification model to be estimated should improve mode

the almost equivalence of pairwise and mutual independence and the duality with exchangeability for a large collection of random variables in an ideal setting pairwise independence is shown to be almost equivalent to mutual independence an asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and asymptotic mutual independence for a triangular array or a sequence of random variables similar equivalence is also presented for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability general unification of multiplicative properties for random variables are obtained the duality between independence and exchangeability is established through the random variables and sample functions in a process implications in other areas are also discussed which include a justification for the use of mutually independent random variables derived from sequential draws where the underlying population only satisfies a version of weak dependence macroscopic stability of some mass phenomena in economics is also characterized via almost mutual independence it is also pointed out that the unit interval can be used to index random variables in the ideal setting provided that it is endowed together with some sample space a suitable larger measure structure

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

prediction of ordinal outcomes when the association between predictors and outcome differs between outcome levels there are a number of regression models which are widely used to predict ordinal outcomes the commonly used models assume that all predictor variables have a similar effect at all levels of the outcome variable if this is not the case for example if some variables predict susceptibility to a disease and others predict the severity of the disease then a more complex model is required one possibility is the multinomial logistic regression model which assumes that the predictor variables have different effects at all levels of the outcome variable an alternative is to use the stereotype family of regression models a one dimensional stereotype model makes the assumption that the effect of each predictor is the same at all outcome levels however it is possible to fit stereotype models with more than one dimension up to a maximum of min k 1 p where k is the number of outcome categories and p is the number of predictor variables a stereotype model of this maximum dimension is equivalent to a multinomial logistic regression model in that it will produce the same predicted values and log likelihood if there are sufficient outcome levels and or predictor variables there may be a number of stereotype models of differing dimension the method is illustrated with an example of prediction of damage to joints in rheumatoid arthritis

reduction from cost sensitive ordinal ranking to weighted binary classification we present a reduction framework from ordinal ranking to binary classification the framework consists of three steps extracting extended examples from the original examples learning a binary classifier on the extended examples with any binary classification algorithm and constructing a ranker from the binary classifier based on the framework we show that a weighted 0 1 loss of the binary classifier upper bounds the mislabeling cost of the ranker both error wise and regret wise our framework allows not only the design of good ordinal ranking algorithms based on well tuned binary classification approaches but also the derivation of new generalization bounds for ordinal ranking from known bounds for binary classification in addition our framework unifies many existing ordinal ranking algorithms such as perceptron ranking and support vector ordinal regression when compared empirically on benchmark data sets some of our newly designed algorithms enjoy advantages in terms of both training speed and generalization performance over existing algorithms in addition the newly designed algorithms lead to better cost sensitive ordinal ranking performance as well as improved listwise ranking performance

bayesian model comparison for the order restricted rc association model association models constitute an attractive alternative to the usual log linear models for modeling the dependence between classification variables they impose special structure on the underlying association by assigning scores on the levels of each classification variable which can be fixed or parametric under the general row column rc association model both row and column scores are unknown parameters without any restriction concerning their ordinality however when the classification variables are ordinal order restrictions on the scores arise naturally under such restrictions we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the bayesian approach to achieve that we have constructed a reversible jump markov chain monte carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging the proposed methodology is evaluated through a simulation study and illustrated using actual datasets

properties of ideal point classification models for bivariate binary data the ideal point classification ipc model was originally proposed for analysing multinomial data in the presence of predictors in this paper we studied properties of the ipc model for analysing bivariate binary data with a specific focus on three quantities 1 the marginal probabilities 2 the association structure between the two binary responses and 3 the joint probabilities we found that the ipc model with a specific class point configuration represents either the marginal probabilities or the association structure however the ipc model is not able to represent both quantities at the same time we then derived a new parametrization of the model the bivariate ipc bipc model which is able to represent both the marginal probabilities and the association structure like the standard ipc model the results of the bipc model can be displayed in a biplot from which the effects of predictors on the binary responses and on their association can be read we will illustrate our findings with a psychological example relating personality traits to depression and anxiety disorders

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

multiple group logistic discrimination among the many possible approaches suggested for statistical discrimination the logistic method can be classified midway between fully distributional solutions of which the assumption of multivariate normality is a classical example 16l and the distribution free techniques using for instance kernel or nearest neighbor methods l 32 therefore it is often called a partially parametric or partially distributional method l l this central position of the logistic model makes it one of the most attractive and widely used tools for solving regression and discrimination problems indeed since there are fewer distributional assumptions than for fully parametric models the logistic method is applicable to a larger family of multivariate distributions involving both discrete and continuous variables moreover in spite of its wide applicability and generality the method remains feasible and easy to use in contrast with nonparametric methods this paper is intended to review the basic ideas and principles of logistic discrimination 415 22 25 and also to bring additional results to some of the queries raised by professor anderson before his death we restrict our attention to discrimination between qualitatively distinct groups and do not envisage the case where groups are quantitatively distinct or ordered 3 12 14 we dedicate this paper to our friend and mentor the late professor j a anderson for his fundamental contribution to discriminant analysis and for his continuous support of our research efforts

a new model for ordinal pain data from a pharmaceutical study for the pain data analysed previously by cox and chuang this paper proposes a new model that assumes monotone scores for ordered response categories this proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison such a model also provides insight regarding the ordinal scale used to classify response estimation of the parameters in the model is obtained by use of bmdp3r

are ordinal models useful for classification there is recent interest in classification procedures intended for use only when the response is ordinal ordinal response however is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses both of which classify either ordinal or non ordinal responses further there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets therefore it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models this paper presents the results of a simulation study designed to compare classification accuracy of various models we show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances until further studies become available we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification

identifying assembly maps in k and l theory in this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in k and l theory and c theory

discriminant analysis when all variables are ordered determination of the equation that relates an ordered dependent variable to ordered independent variables is sought one solution non parametric discriminant analysis npd involves obtaining the best monotonic step function by means of a computer search procedure although one can use alternative selection criteria in obtaining the equation the illustrative examples use absolute distance this paper compares the prediction procedures obtained from npd with those from linear discriminant analysis linear regression with and without transformed variables and logistic regression we show that npd is analogous to regression tree analysis with incorporation of ordered variables and monotonicity we use various prediction functions to predict the example data the data using the leave one out technique and a verification set consistently non parametric discriminant analysis performs as good as or better than the tested alternatives

a log linear model for ordinal data to characterize differential change among treatments we propose a family of log linear models for ordinal data that contain parameters reflecting change patterns to compare treatments relative to change from baseline under the most general model rates of change can depend not only upon the direction of change but also upon the level of the baseline classification we describe methods for selection of a parsimonious model and for tests of hypotheses concerning treatment differences interpretation of treatment differences in the follow up response profiles within baseline strata employs the concept of stochastic ordering data from two clinical trials illustrate the proposed procedure