Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.

Fitting Proportional Odds Models to Educational Data with Complex Sampling Designs in Ordinal Logistic Regression

Abstract: The conventional proportional odds (PO) model assumes that data are collected using simple random sampling by which each sampling unit has the equal probability of being selected from a population. However, when complex survey sampling designs are used, such as stratified sampling, clustered sampling or unequal selection probabilities, it is inappropriate to conduct ordinal logistic regression analyses without taking sampling design into account. Failing to do so may lead to biased estimates of parameters and incorrect corresponding variances. This study illustrates the use of PO models with complex survey data to predict mathematics proficiency levels using Stata and compare the results of PO models accommodating and not accommodating survey sampling features.

On the Consistency of Bayesian Variable Selection for High Dimensional Binary Regression and Classification

Abstract: Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. We use a prior to select a limited number of candidate variables to enter the model, applying a popular method with selection indicators. We show that this approach can induce posterior estimates of the regression functions that are consistently estimating the truth, if the true regression model is sparse in the sense that the aggregated size of the regression coefficients are bounded. The estimated regression functions therefore can also produce consistent classifiers that are asymptotically optimal for predicting future binary outputs. These provide theoretical justifications for some recent empirical successes in microarray data analysis.

Minimum Enclosing Spheres Formulations for Support Vector Ordinal Regression

Abstract: We present two new support vector approaches for ordinal regression. These approaches find the concentric spheres with minimum volume that contain most of the training samples. Both approaches guarantee that the radii of the spheres are properly ordered at the optimal solution. The size of the optimization problem is linear in the number of training samples. The popular SMO algorithm is adapted to solve the resulting optimization problem. Numerical experiments on some real-world data sets verify the usefulness of our approaches for data mining.

Joint association discovery and diagnosis of Alzheimer's disease by supervised heterogeneous multiview learning.

Abstract: A key step for Alzheimer's disease (AD) study is to identify associations between genetic variations and intermediate phenotypes (e.g., brain structures). At the same time, it is crucial to develop a noninvasive means for AD diagnosis. Although these two tasks-association discovery and disease diagnosis-have been treated separately by a variety of approaches, they are tightly coupled due to their common biological basis. We hypothesize that the two tasks can potentially benefit each other by a joint analysis, because (i) the association study discovers correlated biomarkers from different data sources, which may help improve diagnosis accuracy, and (ii) the disease status may help identify disease-sensitive associations between genetic variations and MRI features. Based on this hypothesis, we present a new sparse Bayesian approach for joint association study and disease diagnosis. In this approach, common latent features are extracted from different data sources based on sparse projection matrices and used to predict multiple disease severity levels based on Gaussian process ordinal regression; in return, the disease status is used to guide the discovery of relationships between the data sources. The sparse projection matrices not only reveal the associations but also select groups of biomarkers related to AD. To learn the model from data, we develop an efficient variational expectation maximization algorithm. Simulation results demonstrate that our approach achieves higher accuracy in both predicting ordinal labels and discovering associations between data sources than alternative methods. We apply our approach to an imaging genetics dataset of AD. Our joint analysis approach not only identifies meaningful and interesting associations between genetic variations, brain structures, and AD status, but also achieves significantly higher accuracy for predicting ordinal AD stages than the competing methods.

Evaluating quality measured on a ternary ordinal scale

Abstract: This paper deals with the evaluation of process/product quality measured via a ternary ordinal scale. Recently, a new approach for dealing with ordinal quality variables, based on constructing a quality ladder using rank and dispersion criterion, was proposed. In this method the quality of a given sample is characterized by its relative position on the constructed quality ladder. The present paper proposes a new mechanism for constructing such a quality ladder. This method is called proportion ratio and dispersion (PR&D). The underlying logic, advantage and applications of the proposed method are discussed and demonstrated using software developed by the authors. Copyright © 2008 John Wiley & Sons, Ltd.